Symmetry doi: 10.3390/sym10100429

Authors: Di Ke Yafei Song Wen Quan

The intuitionistic fuzzy set introduced by Atanassov has greater ability in depicting and handling uncertainty. Intuitionistic fuzzy measure is an important research area of intuitionistic fuzzy set theory. Distance measure and similarity measure are two complementary concepts quantifying the difference and closeness of intuitionistic fuzzy sets. This paper addresses the definition of an effective distance measure with concise form and specific meaning for Atanassov&rsquo;s intuitionistic fuzzy sets (AIFSs). A new distance measure for AIFSs is defined based on a distance measure of interval values and the transformation from AIFSs to interval valued fuzzy sets. The axiomatic properties of the new distance measure are mathematically investigated. Comparative analysis based in numerical examples indicates that the new distance measure is competent to quantify the difference between AIFSs. The application of the new distance measure is also discussed. A new method for multi-attribute decision making (MADM) is developed based on the technique for order preference by similarity to an ideal solution method and the new distance measure. Numerical applications indicate that the developed MADM method can obtain reasonable preference orders. This shows that the new distance measure is effective and rational from both mathematical and practical points of view.

]]>Symmetry doi: 10.3390/sym10100428

Authors: Muhammad Gulistan Hafiz Abdul Wahab Florentin Smarandache Salma Khan Sayed Inayat Ali Shah

In this paper, we combined entropy with linguisti neutrosophic cubic numbers and used it in daily life problems related to a corporation that is going to choose an area supervisor, which is the main target of our proposed model. For this, we first develop the theory of linguistic neutrosophic cubic numbers, which explains the indeterminate and incomplete information by truth, indeterminacy and falsity linguistic variables (LVs) for the past, present, as well as for the future time very effectively. After giving the definitions, we initiate some basic operations and properties of linguistic neutrosophic cubic numbers. We also define the linguistic neutrosophic cubic Hamy mean operator and weighted linguistic neutrosophic cubic Hamy mean (WLNCHM) operator with some properties, which can handle multi-input agents with respect to the different time frame. Finally, as an application, we give a numerical example in order to test the applicability of our proposed model.

]]>Symmetry doi: 10.3390/sym10100427

Authors: Tèmítọ́pẹ́ Gbọ́láhàn Jaíyéọlá Emmanuel Ilojide Memudu Olaposi Olatinwo Florentin Smarandache

In this paper, Bol-Moufang types of a particular quasi neutrosophic triplet loop (BCI-algebra), chritened Fenyves BCI-algebras are introduced and studied. 60 Fenyves BCI-algebras are introduced and classified. Amongst these 60 classes of algebras, 46 are found to be associative and 14 are found to be non-associative. The 46 associative algebras are shown to be Boolean groups. Moreover, necessary and sufficient conditions for 13 non-associative algebras to be associative are also obtained: p-semisimplicity is found to be necessary and sufficient for a F 3 , F 5 , F 42 and F 55 algebras to be associative while quasi-associativity is found to be necessary and sufficient for F 19 , F 52 , F 56 and F 59 algebras to be associative. Two pairs of the 14 non-associative algebras are found to be equivalent to associativity ( F 52 and F 55 , and F 55 and F 59 ). Every BCI-algebra is naturally an F 54 BCI-algebra. The work is concluded with recommendations based on comparison between the behaviour of identities of Bol-Moufang (Fenyves&rsquo; identities) in quasigroups and loops and their behaviour in BCI-algebra. It is concluded that results of this work are an initiation into the study of the classification of finite Fenyves&rsquo; quasi neutrosophic triplet loops (FQNTLs) just like various types of finite loops have been classified. This research work has opened a new area of research finding in BCI-algebras, vis-a-vis the emergence of 540 varieties of Bol-Moufang type quasi neutrosophic triplet loops. A &lsquo;Cycle of Algebraic Structures&rsquo; which portrays this fact is provided.

]]>Symmetry doi: 10.3390/sym10100426

Authors: Haiying Wang

The general ( &alpha; , t ) -path sum-connectivity index of a molecular graph originates from many practical problems, such as the three-dimensional quantitative structure&ndash;activity relationships (3D QSAR) and molecular chirality. For arbitrary nonzero real number &alpha; and arbitrary positive integer t, it is defined as t &chi; &alpha; ( G ) = &sum; P t = v i 1 v i 2 ⋯ v i t + 1 &sube; G [ d G ( v i 1 ) d G ( v i 2 ) ⋯ d G ( v i t + 1 ) ] &alpha; , where we take the sum over all possible paths of length t of G and two paths v i 1 v i 2 ⋯ v i t + 1 and v i t + 1 ⋯ v i 2 v i 1 are considered to be one path. In this work, one important class of polycyclic aromatic hydrocarbons and their structures are firstly considered, which play a role in organic materials and medical sciences. We try to compute the exact general ( &alpha; , 2 ) -path sum-connectivity indices of these hydrocarbon systems. Furthermore, we exactly derive the monotonicity and the extremal values of these polycyclic aromatic hydrocarbons for any real number &alpha; . These valuable results could produce strong guiding significance to these applied sciences.

]]>Symmetry doi: 10.3390/sym10100425

Authors: Haihe Ba Huaizhe Zhou Songzhu Mei Huidong Qiao Tie Hong Zhiying Wang Jiangchun Ren

Cloud computing emerges as a change in the business paradigm that offers pay-as-you-go computing capability and brings enormous benefits, but there are numerous organizations showing hesitation for the adoption of cloud computing due to security concerns. Remote attestation has been proven to boost confidence in clouds to guarantee hosted cloud applications&rsquo; integrity. However, the state-of-the-art attestation schemes do not fit that multiple requesters raise their challenges simultaneously, thereby leading to larger performance overheads on the attester side. To address that, we propose an efficient and trustworthy concurrent attestation architecture under multi-requester scenarios, Astrape, to improve efficiency in the integrity and confidentiality protection aspects to generate an unforgeable and encrypted attestation report. Specifically, we propose two key techniques in this paper. The first one&mdash;aggregated attestation signature&mdash;reliably protects the attestation content from being compromised even in the presence of adversaries who have full control of the network, therefore successfully providing attestation integrity. The second one&mdash;delegation-based controlled report&mdash;introduces a third-party service to distribute the attestation report to requesters in order to save computation and communication overload on the attested party. The report is encrypted with an access policy by using attribute-based encryption and accessed by a limited number of qualified requesters, hence supporting attestation confidentiality. The experimental results show that Astrape can take no more than 0.4 s to generate an unforgeable and encrypted report for 1000 requesters and deliver a throughput speedup of approximately 30 &times; in comparison to the existing attestation systems.

]]>Symmetry doi: 10.3390/sym10100424

Authors: Marco Schreck

This work reviews our current understanding of Cherenkov-type processes in vacuum that may occur due to a possible violation of Lorentz invariance. The description of Lorentz violation is based on the Standard Model Extension (SME). To get an overview as general as possible, the most important findings for vacuum Cherenkov radiation in Minkowski spacetime are discussed. After doing so, special emphasis is put on gravitational Cherenkov radiation. For a better understanding, the essential properties of the gravitational SME are recalled in this context. The common grounds and differences of vacuum Cherenkov radiation in Minkowski spacetime and in the gravity sector are emphasized.

]]>Symmetry doi: 10.3390/sym10100423

Authors: Ju Gao Kuang Zhang Guohui Yang Sungtek Kahng Qun Wu

In this paper, a tunable dielectric metamaterial absorber with temperature-based vanadium dioxide (VO2) is proposed. In contrast to previous studies, both the metal phase of VO2 and the semiconductor phase are applied to manipulate the Mie resonant modes in the dielectric cubes. By embedding VO2 in the main resonant structure, the control over Mie resonant modes in dielectric metamaterials is realized. Each resonant mode is analyzed through field distribution and explains why the phase switch of VO2 could affect the absorbance spectrum. This use of tunable materials could create another new methodology for the manipulation of the Mie resonance-based dielectric cubes and make them closer in essence to isotropic metamaterials.

]]>Symmetry doi: 10.3390/sym10100422

Authors: Yuan-Yu Tsai Yu-Shiou Tsai I-Ting Chi Chi-Shiang Chan

The study proposed a vertex-based authentication algorithm based on spatial subdivision. A binary space partitioning tree was employed to subdivide the bounding volume of the input model into voxels. Each vertex could then be encoded into a series of binary digits, denoted as its authentication code, by traversing the constructed tree. Finally, the above authentication code was embedded into the corresponding reference vertex by modulating its position within the located subspace. Extensive experimental results demonstrated that the proposed algorithm provided high embedding capacity and high robustness. Furthermore, the proposed algorithm supported controllable distortion and self-recovery.

]]>Symmetry doi: 10.3390/sym10100421

Authors: Wen-Li Wang Jing-Feng Tian Wing-Sum Cheung

In this thesis, we consider the existence of extreme solutions to a class of coupled causal differential equations. By utilizing two comparison theorems and a monotone iterative technique, we have obtained sufficient conditions under which the equations have extreme solutions. One practical example is presented.

]]>Symmetry doi: 10.3390/sym10090420

Authors: Woncheol Jeong Sergei Alexandrov Lihui Lang

Hill&rsquo;s quadratic orthotropic yield criterion is used for revealing the effect of plastic anisotropy on the distribution of stresses and strains within rotating annular polar orthotropic disks of constant thickness under plane stress. The associated flow rule is adopted for connecting the stresses and strain rates. Assuming that unloading is purely elastic, the distribution of residual stresses and strains is determined as well. The solution for strain rates reduces to one nonlinear ordinary differential equation and two linear ordinary differential equations, even though the boundary value problem involves two independent variables. The aforementioned differential equations can be solved one by one. This significantly simplifies the numerical treatment of the general boundary value problem and increases the accuracy of its solution. In particular, comparison with a finite difference solution is made. It is shown that the finite difference solution is not accurate enough for some applications.

]]>Symmetry doi: 10.3390/sym10090419

Authors: Songtao Shao Xiaohong Zhang Yu Li Chunxin Bo

The uncertainty and concurrence of randomness are considered when many practical problems are dealt with. To describe the aleatory uncertainty and imprecision in a neutrosophic environment and prevent the obliteration of more data, the concept of the probabilistic single-valued (interval) neutrosophic hesitant fuzzy set is introduced. By definition, we know that the probabilistic single-valued neutrosophic hesitant fuzzy set (PSVNHFS) is a special case of the probabilistic interval neutrosophic hesitant fuzzy set (PINHFS). PSVNHFSs can satisfy all the properties of PINHFSs. An example is given to illustrate that PINHFS compared to PSVNHFS is more general. Then, PINHFS is the main research object. The basic operational relations of PINHFS are studied, and the comparison method of probabilistic interval neutrosophic hesitant fuzzy numbers (PINHFNs) is proposed. Then, the probabilistic interval neutrosophic hesitant fuzzy weighted averaging (PINHFWA) and the probability interval neutrosophic hesitant fuzzy weighted geometric (PINHFWG) operators are presented. Some basic properties are investigated. Next, based on the PINHFWA and PINHFWG operators, a decision-making method under a probabilistic interval neutrosophic hesitant fuzzy circumstance is established. Finally, we apply this method to the issue of investment options. The validity and application of the new approach is demonstrated.

]]>Symmetry doi: 10.3390/sym10090418

Authors: Jingqian Wang Xiaohong Zhang

Rough sets provide a useful tool for data preprocessing during data mining. However, many algorithms related to some problems in rough sets, such as attribute reduction, are greedy ones. Matroids propose a good platform for greedy algorithms. Therefore, it is important to study the combination between rough sets and matroids. In this paper, we investigate rough sets and matroids through their operators, and provide a matroidal method for attribute reduction in information systems. Firstly, we generalize four operators of rough sets to four operators of matroids through the interior, closure, exterior and boundary axioms, respectively. Thus, there are four matroids induced by these four operators of rough sets. Then, we find that these four matroids are the same one, which implies the relationship about operators between rough sets and matroids. Secondly, a relationship about operations between matroids and rough sets is presented according to the induced matroid. Finally, the girth function of matroids is used to compute attribute reduction in information systems.

]]>Symmetry doi: 10.3390/sym10090417

Authors: Hu Zhao Hong-Ying Zhang

As a generalization of single value neutrosophic rough sets, the concept of multi-granulation neutrosophic rough sets was proposed by Bo et al., and some basic properties of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators were studied. However, they did not do a comprehensive study on the algebraic structure of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators. In the present paper, we will provide the lattice structure of the pessimistic multigranulation neutrosophic rough approximation operators. In particular, in the one-dimensional case, for special neutrosophic relations, the completely lattice isomorphic relationship between upper neutrosophic rough approximation operators and lower neutrosophic rough approximation operators is proved.

]]>Symmetry doi: 10.3390/sym10090416

Authors: Mario Iglesias-Caamaño Javier Carballo-López Tania Álvarez-Yates Alba Cuba-Dorado Oscar García-García

The development of lateral asymmetries in athletes could have an influence on performance or injuries. The aim of this study was to determine the within-day reliability of the symmetry tests and the performance tests, and explore the relationship between them. Eighteen male volleyball players (18.1 &plusmn; 2.1 years) participated in this study. Seven lateral symmetry assessments were used, namely: lateral symmetry through tensiomyography (LS), active knee extension (AKE), Y-balance test (YBT), muscular electrical activity in attack jump (MEA-AJ), single-leg squat jump (SLSJ), triple hop test for distance (THTD), and bilateral maximum repetition in leg press (1RMSL); and three volleyball performance tests, namely: the T-test, counter-movement jump (CMJ), and attack jump (AJ). Three in-day measurements were taken from each volleyball player after the recovery was completed. The reliability was calculated through the intraclass correlation coefficient and the coefficient of variation, and the relationship was calculated through Pearson&rsquo;s bivariate correlation coefficient (p &lt; 0.05). The results indicate that AKE, YBT, and LS are the symmetry tests with increased reproducibility. THTD correlates positively with the AKE test and 1RMSL test, and a greater symmetry in the YBT correlates with a greater performance in the CMJ and AJ performance tests. In conclusion, AKE, LS, and YBT are the best tests to determine, with reliability, the asymmetries in volleyball players, and a greater symmetry in the YBT seems to influence the height of bilateral vertical jump.

]]>Symmetry doi: 10.3390/sym10090415

Authors: Yoh Tanimoto

We construct families of ground state representations of the U ( 1 ) -current net and of the Virasoro nets Vir c with central charge c &ge; 1 . We show that these representations are not covariant with respect to the original dilations, and those on the U ( 1 ) -current net are not solitonic. Furthermore, by going to the dual net with respect to the ground state representations of Vir c , one obtains possibly new family of M&ouml;bius covariant nets on S 1 .

]]>Symmetry doi: 10.3390/sym10090414

Authors: Traian Caramihale Dan Popescu Loretta Ichim

The detection of human emotions has applicability in various domains such as assisted living, health monitoring, domestic appliance control, crowd behavior tracking real time, and emotional security. The paper proposes a new system for emotion classification based on a generative adversarial network (GAN) classifier. The generative adversarial networks have been widely used for generating realistic images, but the classification capabilities have been vaguely exploited. One of the main advantages is that by using the generator, we can extend our testing dataset and add more variety to each of the seven emotion classes we try to identify. Thus, the novelty of our study consists in increasing the number of classes from N to 2N (in the learning phase) by considering real and fake emotions. Facial key points are obtained from real and generated facial images, and vectors connecting them with the facial center of gravity are used by the discriminator to classify the image as one of the 14 classes of interest (real and fake for seven emotions). As another contribution, real images from different emotional classes are used in the generation process unlike the classical GAN approach which generates images from simple noise arrays. By using the proposed method, our system can classify emotions in facial images regardless of gender, race, ethnicity, age and face rotation. An accuracy of 75.2% was obtained on 7000 real images (14,000, also considering the generated images) from multiple combined facial datasets.

]]>Symmetry doi: 10.3390/sym10090413

Authors: Nurbige Turan Necati Olgun

Let k be an algebraically closed field of characteristic zero, and R / I and S / J be algebras over k . Ω 1 ( R / I ) and Ω 1 ( S / J ) denote universal module of first order derivation over k . The main result of this paper asserts that the first nonzero Fitting ideal Ω 1 ( R / I &otimes; k S / J ) is an invertible ideal, if the first nonzero Fitting ideals Ω 1 ( R / I ) and Ω 1 ( S / J ) are invertible ideals. Then using this result, we conclude that the projective dimension of Ω 1 ( R / I &otimes; k S / J ) is less than or equal to one.

]]>Symmetry doi: 10.3390/sym10090411

Authors: Alexander B. Balakin Alexei S. Ilin

We study a new exactly solvable model of coupling of the Dark Energy and Dark Matter, in the framework of which the kernel of non-gravitational interaction is presented by the integral Volterra-type operator well-known in the classical theory of fading memory. Exact solutions of this isotropic homogeneous cosmological model were classified with respect to the sign of the discriminant of the cubic characteristic polynomial associated with the key equation of the model. Energy-density scalars of the Dark Energy and Dark Matter, the Hubble function and acceleration parameter are presented explicitly; the scale factor is found in quadratures. Asymptotic analysis of the exact solutions has shown that the Big Rip, Little Rip, Pseudo Rip regimes can be realized with the specific choice of guiding parameters of the model. We show that the Coincidence problem can be solved if we consider the memory effect associated with the interactions in the Dark Sector of the universe.

]]>Symmetry doi: 10.3390/sym10090412

Authors: Naige Wang Guohua Cao Lu Yan Lei Wang

The modeling and control of the multi-rope parallel suspension lifting system (MPSLS) are investigated in the presence of different and spatial distributed tensions; unknown boundary disturbances; and multiple constraints, including time varying geometric constraint, input saturation, and output constraint. To describe the system dynamics more accurately, the MPSLS is modelled by a set of partial differential equations and ordinary differential equations (PDEs-ODEs) with multiple constraints, which is a nonhomogeneous and coupled PDEs-ODEs, and makes its control more difficult. Adaptive boundary control is a recommended method for position regulation and vibration degradation of the MPSLS, where adaptation laws and a boundary disturbance observer are formulated to handle system uncertainties. The system stability is rigorously proved by using Lyapunov&rsquo;s direct method, and the position and vibration eventually diminish to a bounded neighborhood of origin. The original PDEs-ODEs are solved by finite difference method, and the multiple constraints problem is processed simultaneously. Finally, the performance of the proposed control is demonstrated by both the results of ADAMS simulation and numerical calculation.

]]>Symmetry doi: 10.3390/sym10090410

Authors: Ewald Hejl Friedrich Finger

Chromatographic interaction between infiltrating solutions of racemic mixtures of enantiomers and enantiomorphic minerals with chiral excess has been proposed as a scenario for the emergence of biomolecular homochirality. Enantiomer separation is supposed to be produced by different partition coefficients of both enantiomers with regard to crystal faces or walls of capillary tubes in the enantiomorphic mineral. Besides quartz, nepheline is the only common magmatic mineral with enantiomorphic symmetry. It crystallizes from SiO2-undersaturated melts with low viscosity and is a promising candidate for chiral enrichment by autocatalytic secondary nucleation. Under liquidus conditions, the dynamic viscosity of silicate melts is mainly a function of polymerization. Melts with low concentrations of SiO2 (&lt;55 wt%) and rather high concentrations of Na2O (&gt;7 wt%) are only slightly polymerized and hence are characterized by low viscosities. Such melts can ascend, intrude or extrude by turbulent flow. Fourteen volcanic and subvolcanic samples from alkaline provinces in Africa and Sweden were chemically analyzed. Polished thin sections containing fresh nepheline phenocrysts were etched with 1% hydrofluoric acid at 20 &deg;C for 15 to 25 min. Nepheline crystals suitable for a statistical evaluation of their etch figures were found in four samples. Crystals with chiral etch figures are mainly not twinned. Their chiral proportions in grain percentages of single crystals are close to parity in three samples. Only one sample shows a slight chiral excess (41.67% L-type vs. 58.33% D-type) but at a low level of significance (15 vs. 21 crystals, respectively).

]]>Symmetry doi: 10.3390/sym10090409

Authors: Dejian Huang Yanqing Li Donghe Pei

This paper investigates the boundary value in the heat conduction problem by a variational iteration method. Applying the iteration method, a sequence of convergent functions is constructed, the limit approximates the exact solution of the heat conduction equation in a few iterations using only the initial condition. This method does not require discretization of the variables. Numerical results show that this method is quite simple and straightforward for models that are currently under research.

]]>Symmetry doi: 10.3390/sym10090408

Authors: Qianqian Xing Baosheng Wang Xiaofeng Wang

Without the design for inherent security, the Border Gateway Protocol (BGP) is vulnerable to prefix/subprefix hijacks and other attacks. Though many BGP security approaches have been proposed to prevent or detect such attacks, the unsatisfactory cost-effectiveness frustrates their deployment. In fact, the currently deployed BGP security infrastructure leaves the chance for potential centralized authority misconfiguration and abuse. It actually becomes the critical yield point that demands the logging and auditing of misbehaviors and attacks in BGP security deployments. We propose a blockchain-based Internet number resource authority and trustworthy management solution, named BGPcoin, to facilitate the transparency of BGP security. BGPcoin provides a reliable origin advertisement source for origin authentication by dispensing resource allocations and revocations compliantly against IP prefix hijacking. We perform and audit resource assignments on the tamper-resistant Ethereum blockchain by means of a set of smart contracts, which also interact as one to provide the trustworthy origin route examination for BGP. Compared with RPKI, BGPcoin yields significant benefits in securing origin advertisement and building a dependable infrastructure for the object repository. We demonstrate it through an Ethereum prototype implementation, and we deploy it and do experiment on a locally-simulated network and an official Ethereum test network respectively. The extensive experiment and evaluation demonstrate the incentives to deploy BGPcoin, and the enhanced security provided by BGPcoin is technically and economically feasible.

]]>Symmetry doi: 10.3390/sym10090407

Authors: Wenchao Jiang Yinhu Zhai Zhigang Zhuang Paul Martin Zhiming Zhao Jia-Bao Liu

The generalization of Farey graphs and extended Farey graphs all originate from Farey graphs. They are simultaneously scale-free and small-world. A labeling of the vertices for them are proposed here. All of the shortest paths between any two vertices in these two graphs can be determined only on their labels. The number of shortest paths between any two vertices is the product of two Fibonacci numbers; it is increasing almost linearly with the order or size of the graphs. However, the label-based routing algorithm runs in logarithmic time O(logn). Our efficient routing protocol for Farey-type models should help contribute toward the understanding of several physical dynamic processes.

]]>Symmetry doi: 10.3390/sym10090406

Authors: Xiaoliang Xie Jiali He

Soft set theory is a mathematical tool for handling uncertainty. This paper investigates the limits of the interval type of soft sets ( i t -soft sets). The notion of i t -soft sets is first introduced. Then, the limits of i t -soft sets are proposed and their properties obtained. Next, point-wise continuity of i t -soft sets and continuous i t -soft sets is discussed. Finally, an application for rough sets is given.

]]>Symmetry doi: 10.3390/sym10090405

Authors: Mobeen Munir Asim Naseem Akhtar Rasool Muhammad Shoaib Saleem Shin Min Kang

Fixed points of functions have applications in game theory, mathematics, physics, economics and computer science. The purpose of this article is to compute fixed points of a general quadratic polynomial in finite algebras of split quaternion and octonion over prime fields Z p. Some characterizations of fixed points in terms of the coefficients of these polynomials are also given. Particularly, cardinalities of these fixed points have been determined depending upon the characteristics of the underlying field.

]]>Symmetry doi: 10.3390/sym10090404

Authors: Musavarah Sarwar Muhammad Akram Noura Omair Alshehri

Hypergraph theory is the most developed tool for demonstrating various practical problems in different domains of science and technology. Sometimes, information in a network model is uncertain and vague in nature. In this paper, our main focus is to apply the powerful methodology of fuzziness to generalize the notion of competition hypergraphs and fuzzy competition graphs. We introduce various new concepts, including fuzzy column hypergraphs, fuzzy row hypergraphs, fuzzy competition hypergraphs, fuzzy k-competition hypergraphs and fuzzy neighbourhood hypergraphs, strong hyperedges, kth strength of competition and symmetric properties. We design certain algorithms for constructing different types of fuzzy competition hypergraphs. We also present applications of fuzzy competition hypergraphs in decision support systems, including predator&ndash;prey relations in ecological niche, social networks and business marketing.

]]>Symmetry doi: 10.3390/sym10090403

Authors: Muhammad Aslam Osama H. Arif

Parts manufacturers use sudden death testing to reduce the testing time of experiments. The sudden death testing plan in the literature can only be applied when all observations of failure time/parameters are crisp. In practice however, it is noted that not all measurements of continuous variables are precise. Therefore, the existing sudden death test plan can be applied if failure data/or parameters are imprecise, incomplete, and fuzzy. The classical statistics have the special case of neutrosophic statistics when there are no fuzzy observations/parameters. The neutrosophic fuzzy statistics can be applied for the testing of manufacturing parts when observations are imprecise, incomplete and fuzzy. In this paper, we will design an original neutrosophic fuzzy sudden death testing plan for the inspection/testing of the electronic product or parts manufacturing. We will assume that the lifetime of the product follows the neutrosophic fuzzy Weibull distribution. The neutrosophic fuzzy operating function will be given and used to determine the neutrosophic fuzzy plan parameters through a neutrosophic fuzzy optimization problem. The results of the proposed neutrosophic fuzzy death testing plan will be implemented with the aid of an example.

]]>Symmetry doi: 10.3390/sym10090402

Authors: Yongju Choi Othmane Atif Jonguk Lee Daihee Park Yongwha Chung

Sound-event classification has emerged as an important field of research in recent years. In particular, investigations using sound data are being conducted in various industrial fields. However, sound-event classification tasks have become more difficult and challenging with the increase in noise levels. In this study, we propose a noise-robust system for the classification of sound data. In this method, we first convert one-dimensional sound signals into two-dimensional gray-level images using normalization, and then extract the texture images by means of the dominant neighborhood structure (DNS) technique. Finally, we experimentally validate the noise-robust approach by using four classifiers (convolutional neural network (CNN), support vector machine (SVM), k-nearest neighbors(k-NN), and C4.5). The experimental results showed superior classification performance in noisy conditions compared with other methods. The F1 score exceeds 98.80% in railway data, and 96.57% in livestock data. Besides, the proposed method can be implemented in a cost-efficient manner (for instance, use of a low-cost microphone) while maintaining high level of accuracy in noisy environments. This approach can be used either as a standalone solution or as a supplement to the known methods to obtain a more accurate solution.

]]>Symmetry doi: 10.3390/sym10090401

Authors: Sukhveer Singh Harish Garg

Type-2 intuitionistic fuzzy set (T2IFS) is a powerful and important extension of the classical fuzzy set, intuitionistic fuzzy set to measure the vagueness and uncertainty. In a practical decision-making process, there always occurs an inter-relationship among the multi-input arguments. To deal with this point, the motivation of the present paper is to develop some new interval type-2 (IT2) intuitionistic fuzzy aggregation operators which can consider the multi interaction between the input argument. To achieve it, we define a symmetric triangular interval T2IFS (TIT2IFS), its operations, Hamy mean (HM) operator to aggregate the preference of the symmetric TIT2IFS and then shows its applicability through a multi-criteria decision making (MCDM). Several enviable properties and particular cases together with following different parameter values of this operator are calculated in detail. At last a numerical illustration is to given to exemplify the practicability of the proposed technique and a comparative analysis is analyzed in detail.

]]>Symmetry doi: 10.3390/sym10090400

Authors: Jungho Kim Yadav Sunil Kumar Jisang Yoo Soonchul Kwon

The eye blink rate, a major human physiological response, directly affects ocular diseases, such as keratitis and dry eye syndrome. It has been shown that the eye blink rate in normal eyes has a certain frequency for individuals, from 6&ndash;30 times/min. It was suggested in a previous study that the eye blink rate can be decreased during the viewing of high-intensity and realistic content. Therefore, in this paper, we examine the change of the eye blink rate during the HMD (head-mounted display) viewing of VR (virtual reality) contents; accordingly, we propose an algorithm to measure the eye blink rate as well as compare and analyze this rate in three different environments (natural, monitor, and HMD). We confirmed that IPD (interpupillary distance) and phoria affected the eye blink rate in each environment. In this experiment, 21 subjects (28.38 &plusmn; 6.87 years) were selected, and a paired t-test was performed for changes in the eye blink rate over 1 min for each environment. The IPD and phoria effects on the eye blink rate were confirmed using the Spearman&rsquo;s correlation coefficient. In this experiment, the eye blink rate was decreased in the monitor and HMD environments compared with the natural environment, while that in the HMD environment was decreased compared with the monitor environment. The results of the correlation analysis of far IPD and the eye blink rate show no statistical significance or correlation. The correlation analysis of near IPD and the eye blink rate showed a strong positive correlation of the eye blink rate in the monitor environment. The correlation analysis of distance phoria and the eye blink rate showed a strong negative correlation of the eye blink rate in the HMD environment. The correlation analysis of near-field phoria and the eye blink rate showed a strong negative correlation of the eye blink rate in the HMD environment. It is expected that the results of this study will be used as a VR-viewing recommendation.

]]>Symmetry doi: 10.3390/sym10090399

Authors: Congxu Zhu Guojun Wang Kehui Sun

This article performs the cryptanalysis of an image encryption algorithm using an S-box generated by chaos. The algorithm has the advantages of simple structure, high encryption efficiency, and good encryption performance. However, an attentive investigation reveals that it has some undiscovered security flaws. The image cryptosystem is totally breakable under proposed chosen-plaintext attack, and only two chosen plain-images are required. An array equivalent to the S-box is constructed by an elaborately designed chosen-plaintext image, and the cipher-image is deciphered without having to know the S-box itself. Both mathematical deduction and experimental results validate the feasibility of the attacking scheme. Furthermore, an improved encryption scheme is proposed, in which a feedback mechanism is introduced, a bidirectional diffusion scheme is designed, and values of the ciphertext are associated with more parameters in each diffusion process. Testing results and security analysis verify that the improved cryptographic system can achieve a higher security level and has a better performance than some of the latest encryption algorithms.

]]>Symmetry doi: 10.3390/sym10090398

Authors: Erhan Güler Hasan Hilmi Hacısalihoğlu Young Ho Kim

We study and examine the rotational hypersurface and its Gauss map in Euclidean four-space E 4 . We calculate the Gauss map, the mean curvature and the Gaussian curvature of the rotational hypersurface and obtain some results. Then, we introduce the third Laplace&ndash;Beltrami operator. Moreover, we calculate the third Laplace&ndash;Beltrami operator of the rotational hypersurface in E 4 . We also draw some figures of the rotational hypersurface.

]]>Symmetry doi: 10.3390/sym10090397

Authors: Xiang Hou Lianquan Min Hui Yang

To protect the security of vector maps, we propose a novel reversible watermarking scheme for vector maps based on a multilevel histogram modification. First, a difference histogram is constructed using the correlations of adjacent coordinates, and the histogram is divided into continuous regions and discontinuous regions by combining the characteristics of vector map data. Second, the histogram bins that require modification are determined in the continuous regions through the optimal peak value, and the peak values are chosen from the flanking discontinuous regions in both directions; the watermarks are embedded by adopting the multilevel histogram modification strategy. The watermark extraction process is the reverse of the embedding process, and after completing the watermark extraction, the carrier data can be recovered losslessly. The experimental results show that the proposed algorithm has good invisibility and is completely reversible. Compared with similar algorithms reported previously, it achieves higher watermark embedding capacity under the same embedding distortion with lower complexity, thereby having a higher application value.

]]>Symmetry doi: 10.3390/sym10090396

Authors: Taisaku Mori Shin’ichi Nojiri

Recently, we have proposed models of topological field theory including gravity in Mod. Phys. Lett. A 2016, 31, 1650213 and Phys. Rev. D 2017, 96, 024009, in order to solve the problem of the cosmological constant. The Lagrangian densities of the models are BRS (Becchi-Rouet-Stora) exact and therefore the models can be regarded as topological theories. In the models, the coupling constants, including the cosmological constant, look as if they run with the scale of the universe and its behavior is very similar to the renormalization group. Motivated by these models, we propose new models with an the infrared fixed point, which may correspond to the late time universe, and an ultraviolet fixed point, which may correspond to the early universe. In particular, we construct a model with the solutions corresponding to the de Sitter space-time both in the ultraviolet and the infrared fixed points.

]]>Symmetry doi: 10.3390/sym10090395

Authors: Cheon Seoung Ryoo

The goal of this paper is to define the ( p , q ) -analogue of tangent numbers and polynomials by generalizing the tangent numbers and polynomials and Carlitz-type q-tangent numbers and polynomials. We get some explicit formulas and properties in conjunction with ( p , q ) -analogue of tangent numbers and polynomials. We give some new symmetric identities for ( p , q ) -analogue of tangent polynomials by using ( p , q ) -tangent zeta function. Finally, we investigate the distribution and symmetry of the zero of ( p , q ) -analogue of tangent polynomials with numerical methods.

]]>Symmetry doi: 10.3390/sym10090394

Authors: Dan Huang Xiangxuan Liu Zheng Xie Xuanjun Wang Xin Gao Yuxue Yang

The toxic transformation products of hydrazines are of great concern. These products&rsquo; properties combined with their formation mechanisms are needed to assess their potential environmental and human impacts. In this study, the gas-phase reaction of hydrazine (N2H4), monomethyldrazine (MMH) and unsymmetrical dimethyhydrazine (UDMH) with O3 have been studied at varying reactant ratios, both in the presence and absence of a radical trap. Gas chromatography-mass spectroscopy (GC-MS) has been implied to follow reactant consumption and product formation. Apart from the reported products detected by Fourier transform infrared spectroscopy (FT-IR), the newly found compounds (hydrazones, formamides, dimethylamine, 1,1,4,4-tetramethyl-1,2-tetrazene,dimethylamino-acetonitrile, N2, H2O, et al.) are identified by GC-MS. The relative yields of the organic products vary considerably at different O3/MMH or UDMH ratios. UDMH and MMH are confirmed as high potential precursors of N-nitrosodimethylamine (NDMA). The presence of hydroxyl radicals (HO&middot;) hinders NDMA formation in MMH-O3 system. Meanwhile, it increases NDMA formation in UDMH-O3 system. The suggested reaction mechanisms which account for the observed products are discussed.

]]>Symmetry doi: 10.3390/sym10090393

Authors: Dragan Pamučar Željko Stević Siniša Sremac

In this paper, a new multi-criteria problem solving method&mdash;the Full Consistency Method (FUCOM)&mdash;is proposed. The model implies the definition of two groups of constraints that need to satisfy the optimal values of weight coefficients. The first group of constraints is the condition that the relations of the weight coefficients of criteria should be equal to the comparative priorities of the criteria. The second group of constraints is defined on the basis of the conditions of mathematical transitivity. After defining the constraints and solving the model, in addition to optimal weight values, a deviation from full consistency (DFC) is obtained. The degree of DFC is the deviation value of the obtained weight coefficients from the estimated comparative priorities of the criteria. In addition, DFC is also the reliability confirmation of the obtained weights of criteria. In order to illustrate the proposed model and evaluate its performance, FUCOM was tested on several numerical examples from the literature. The model validation was performed by comparing it with the other subjective models (the Best Worst Method (BWM) and Analytic Hierarchy Process (AHP)), based on the pairwise comparisons of the criteria and the validation of the results by using DFC. The results show that FUCOM provides better results than the BWM and AHP methods, when the relation between consistency and the required number of the comparisons of the criteria are taken into consideration. The main advantages of FUCOM in relation to the existing multi-criteria decision-making (MCDM) methods are as follows: (1) a significantly smaller number of pairwise comparisons (only n &minus; 1), (2) a consistent pairwise comparison of criteria, and (3) the calculation of the reliable values of criteria weight coefficients, which contribute to rational judgment.

]]>Symmetry doi: 10.3390/sym10090392

Authors: M. G. Abbas Malik Zia Bashir Tabasam Rashid Jawad Ali

Decision making is the key component of people&rsquo;s daily life, from choosing a mobile phone to engaging in a war. To model the real world more accurately, probabilistic linguistic term sets (PLTSs) were proposed to manage a situation in which several possible linguistic terms along their corresponding probabilities are considered at the same time. Previously, in linguistic term sets, the probabilities of all linguistic term sets are considered to be equal which is unrealistic. In the process of decision making, due to the vagueness and complexity of real life, an expert usually hesitates and unable to express its opinion in a single term, thus making it difficult to reach a final agreement. To handle real life scenarios of a more complex nature, only membership linguistic decision making is unfruitful; thus, some mechanism is needed to express non-membership linguistic term set to deal with imprecise and uncertain information in more efficient manner. In this article, a novel notion called probabilistic hesitant intuitionistic linguistic term set (PHILTS) is designed, which is composed of membership PLTSs and non-membership PLTSs describing the opinions of decision makers (DMs). In the theme of PHILTS, the probabilities of membership linguistic terms and non-membership linguistic terms are considered to be independent. Then, basic operations, some governing operational laws, the aggregation operators, normalization process and comparison method are studied for PHILTSs. Thereafter, two practical decision making models: aggregation based model and the extended TOPSIS model for PHILTS are designed to classify the alternatives from the best to worst, as an application of PHILTS to multi-attribute group decision making. In the end, a practical problem of real life about the selection of the best alternative is solved to illustrate the applicability and effectiveness of our proposed set and models.

]]>Symmetry doi: 10.3390/sym10090391

Authors: Siqi Liu Boliang Lin Jianping Wu Yinan Zhao

As air pollution becomes increasingly severe, express trains play a more important role in shifting road freight and reducing carbon emissions. Thus, the design of railway express shipment service networks has become a key issue, which needs to be addressed urgently both in theory and practice. The railway express shipment service network design problem (RESSNDP) not only involves the selection of train services and determination of service frequency, but it is also associated with shipment routing, which can be viewed as a service network design problem (SNDP) with railway characteristics. This paper proposes a non-linear integer programming model (INLP) which aims at finding a service network and shipment routing plan with minimum cost while satisfying the transportation time constraints of shipments, carrying capacity constraints of train services, flow conservation constraint and logical constraints among decision variables. In addition, a linearization technique was adopted to transform our model into a linear one to obtain a global optimal solution. To evaluate the effectiveness and efficiency of our approach, a small trial problem was solved by the state-of-the-art mathematical programming solver Gurobi 7.5.2.

]]>Symmetry doi: 10.3390/sym10090390

Authors: Emily R. Boeving Eliza L. Nelson

Reports of lateralized behavior are widespread, although the majority of findings have focused on the visual or motor domains. Less is known about laterality with regards to the social domain. We previously observed a left-side bias in two social affiliative behaviors&mdash;embrace and face-embrace&mdash;in captive Colombian spider monkeys (Ateles fusciceps rufiventris). Here we applied social network analysis to laterality for the first time. Our findings suggest that laterality influences social structure in spider monkeys with structural differences between networks based on direction of behavioral bias and social interaction type. We attribute these network differences to a graded spectrum of social risk comprised of three dimensions.

]]>Symmetry doi: 10.3390/sym10090389

Authors: Juan C. Sánchez-Hernández José Agustín Pacheco-Ortiz Leonardo Rodríguez-Sosa Gabina Calderón-Rosete Edgar Villagran-Vargas

Recent studies have postulated that the left and right caudal photoreceptors (CPR-L and CPR-R, respectively) of the crayfish show asymmetry of spontaneous activity in darkness and responses induced by white light. Two photopigments have been identified; the first one sensitive to blue light and the second one sensitive to green light. This study explores blue and green monochromatic light responsiveness with respect to both CPR-L and -R, as well as the effects of temperature on these photoreceptors. We performed simultaneous extracellular recordings of the firing rate of action potentials from CPRs of the crayfish Cherax quadricarinatus (n = 12). At room temperature (24 &plusmn; 1 &deg;C), CPR-L and -R showed a significant difference in the spikes from most of the comparations. CPRs in the dark exhibited spontaneous asymmetric activity and displayed sensitivity to both monochromatic light sources. CPR responses were light intensity dependent within a range of 1.4 logarithmic intensity units, showing approximately 0.5 logarithmic intensity units more sensitivity to blue than to green light. The CPRs displayed an asymmetrical response to both colors by using a constant light intensity. At 14 (&plusmn;1) &deg;C, activity in darkness diminished while asymmetry persisted, and the CPRs improved responses for both monochromatic light sources, displaying a significant asymmetry. Here, we provide additional evidence of the asymmetric activity in darkness and light response from the CPRs. The new data allow further investigations regarding the physiological role of caudal photoreceptors in the crayfish.

]]>Symmetry doi: 10.3390/sym10090388

Authors: Marco V. José Gabriel S. Zamudio

It has long been claimed that the mitochondrial genetic code possesses more symmetries than the Standard Genetic Code (SGC). To test this claim, the symmetrical structure of the SGC is compared with noncanonical genetic codes. We analyzed the symmetries of the graphs of codons and their respective phenotypic graph representation spanned by the RNY (R purines, Y pyrimidines, and N any of them) code, two RNA Extended codes, the SGC, as well as three different mitochondrial genetic codes from yeast, invertebrates, and vertebrates. The symmetry groups of the SGC and their corresponding phenotypic graphs of amino acids expose the evolvability of the SGC. Indeed, the analyzed mitochondrial genetic codes are more symmetrical than the SGC.

]]>Symmetry doi: 10.3390/sym10090387

Authors: Jose Luis Espinosa-Aranda Noelia Vallez Jose Maria Rico-Saavedra Javier Parra-Patino Gloria Bueno Matteo Sorci David Moloney Dexmont Pena Oscar Deniz

Computer vision and deep learning are clearly demonstrating a capability to create engaging cognitive applications and services. However, these applications have been mostly confined to powerful Graphic Processing Units (GPUs) or the cloud due to their demanding computational requirements. Cloud processing has obvious bandwidth, energy consumption and privacy issues. The Eyes of Things (EoT) is a powerful and versatile embedded computer vision platform which allows the user to develop artificial vision and deep learning applications that analyse images locally. In this article, we use the deep learning capabilities of an EoT device for a real-life facial informatics application: a doll capable of recognizing emotions, using deep learning techniques, and acting accordingly. The main impact and significance of the presented application is in showing that a toy can now do advanced processing locally, without the need of further computation in the cloud, thus reducing latency and removing most of the ethical issues involved. Finally, the performance of the convolutional neural network developed for that purpose is studied and a pilot was conducted on a panel of 12 children aged between four and ten years old to test the doll.

]]>Symmetry doi: 10.3390/sym10090386

Authors: Walaa Alajali Wei Zhou Sheng Wen Yu Wang

Traffic prediction is a critical task for intelligent transportation systems (ITS). Prediction at intersections is challenging as it involves various participants, such as vehicles, cyclists, and pedestrians. In this paper, we propose a novel approach for the accurate intersection traffic prediction by introducing extra data sources other than road traffic volume data into the prediction model. In particular, we take advantage of the data collected from the reports of road accidents and roadworks happening near the intersections. In addition, we investigate two types of learning schemes, namely batch learning and online learning. Three popular ensemble decision tree models are used in the batch learning scheme, including Gradient Boosting Regression Trees (GBRT), Random Forest (RF) and Extreme Gradient Boosting Trees (XGBoost), while the Fast Incremental Model Trees with Drift Detection (FIMT-DD) model is adopted for the online learning scheme. The proposed approach is evaluated using public data sets released by the Victorian Government of Australia. The results indicate that the accuracy of intersection traffic prediction can be improved by incorporating nearby accidents and roadworks information.

]]>Symmetry doi: 10.3390/sym10090385

Authors: Yoosoo Jeong Seungmin Lee Daejin Park Kil Houm Park

Recently, there have been many studies on the automatic extraction of facial information using machine learning. Age estimation from frontal face images is becoming important, with various applications. Our proposed work is based on a binary classifier that only determines whether two input images are clustered in a similar class and trains a convolutional neural network (CNN) model using the deep metric learning method based on the Siamese network. To converge the results of the training Siamese network, two classes, for which age differences are below a certain level of distance, are considered as the same class, so the ratio of positive database images is increased. The deep metric learning method trains the CNN model to measure similarity based only on age data, but we found that the accumulated gender data can also be used to compare ages. Thus, we adopted a multi-task learning approach to consider the gender data for more accurate age estimation. In the experiment, we evaluated our approach using MORPH and MegaAge-Asian datasets, and compared gender classification accuracy only using age data from the training images. In addition, using gender classification, our proposed architecture, which is trained with only age data, performs age comparison using the self-generated gender feature. The accuracy enhancement by multi-task learning, i.e. simultaneously considering age and gender data, is discussed. Our approach results in the best accuracy among the methods based on deep metric learning on MORPH dataset. Additionally, our method has better results than the state of the art in terms of age estimation on MegaAge-Asian and MORPH datasets.

]]>Symmetry doi: 10.3390/sym10090384

Authors: Ali Namakin Seyyed Esmaeil Najafi Mohammad Fallah Mehrdad Javadi

There are numerous models for solving the efficiency evaluation in data envelopment analysis (DEA) with fuzzy input and output data. However, because of the limitation of those strategies, they cannot be implemented for solving fully fuzzy DEA (FFDEA). Furthermore, in real-world problems with imprecise data, fuzziness is not sufficient to consider, and the reliability of the information is also very vital. To overcome these flaws, this paper presented a new method for solving the fully fuzzy DEA model where all parameters are Z-numbers. The new approach is primarily based on crisp linear programming and has a simple structure. Moreover, it is proved that the only existing method to solve FFDEA with Z-numbers is not valid. An example is also presented to illustrate the efficiency of our proposed method and provide an explanation for the content of the paper.

]]>Symmetry doi: 10.3390/sym10090383

Authors: Kaiyuan Bai Xiaomin Zhu Jun Wang Runtong Zhang

In respect to the multi-attribute group decision making (MAGDM) problems in which the evaluated value of each attribute is in the form of q-rung orthopair fuzzy numbers (q-ROFNs), a new approach of MAGDM is developed. Firstly, a new aggregation operator, called the partitioned Maclaurin symmetric mean (PMSM) operator, is proposed to deal with the situations where the attributes are partitioned into different parts and there are interrelationships among multiple attributes in same part whereas the attributes in different parts are not related. Some desirable properties of PMSM are investigated. Then, in order to aggregate the q-rung orthopair fuzzy information, the PMSM is extended to q-rung orthopair fuzzy sets (q-ROFSs) and two q-rung orthopair fuzzy partitioned Maclaurin symmetric mean (q-ROFPMSM) operators are developed. To eliminate the negative influence of unreasonable evaluation values of attributes on aggregated result, we further propose two q-rung orthopair fuzzy power partitioned Maclaurin symmetric mean (q-ROFPPMSM) operators, which combine the PMSM with the power average (PA) operator within q-ROFSs. Finally, a numerical instance is provided to illustrate the proposed approach and a comparative analysis is conducted to demonstrate the advantage of the proposed approach.

]]>Symmetry doi: 10.3390/sym10090382

Authors: Kris Coolsaet Stan Schein

The icosahedron and the dodecahedron have the same graph structures as their algebraic conjugates, the great dodecahedron and the great stellated dodecahedron. All four polyhedra are equilateral and have planar faces&mdash;thus &ldquo;EP&rdquo;&mdash;and display icosahedral symmetry. However, the latter two (star polyhedra) are non-convex and &ldquo;pathological&rdquo; because of intersecting faces. Approaching the problem analytically, we sought alternate EP-embeddings for Platonic and Archimedean solids. We prove that the number of equations&mdash;E edge length equations (enforcing equilaterality) and 2 E &minus; 3 F face (torsion) equations (enforcing planarity)&mdash;and of variables ( 3 V &minus; 6 ) are equal. Therefore, solutions of the equations up to equivalence generally leave no degrees of freedom. As a result, in general there is a finite (but very large) number of solutions. Unfortunately, even with state-of-the-art computer algebra, the resulting systems of equations are generally too complicated to completely solve within reasonable time. We therefore added an additional constraint, symmetry, specifically requiring solutions to display (at least) tetrahedral symmetry. We found 77 non-classical embeddings, seven without intersecting faces&mdash;two, four and one, respectively, for the (graphs of the) dodecahedron, the icosidodecahedron and the rhombicosidodecahedron.

]]>Symmetry doi: 10.3390/sym10090381

Authors: Wei Han Gang Wang Chuanzheng Liu Hengjie Luan Ke Wang

Under the effect of initial stress and excavation disturbance, there exists interaction between rock mass and rockbolt in deeply buried tunnels. In order to fully explore the mechanism of rock mass supported with rockbolts, this article studied the time-dependent behavior of the rock mass supported with discretely mechanically or frictionally coupled (DMFC) rockbolts. The interaction model elastic solutions under distributed force model were analyzed, then the viscoelastic analytical solutions were conducted to describe the rheological properties of the coupling model, and the solutions were acquired by setting the constitutive models of the rockbolt and rock mass in terms of a one-dimensional Kelvin model and a three-dimensional Burgers model based on material properties and dimension. Several examples were performed and the influence of initial stress &sigma;0, the viscosity parameters &eta;1 and &eta;2 of the three-dimensional Burgers model as well as the pre-tension T0 on reinforcement effect were analyzed. According to the proposed model, the smaller &eta;2 is or the larger the pre-tension T0 is, the more effective the support effect. However, when the pre-tension is too large, the support effect is no longer significantly enhanced. In addition, the early reinforcement effect is controlled by the first creep stage in the Burgers model while the ultimate support effect is mainly influenced by the viscosity coefficient of the second creep stage in the Burgers model. This research can provide an important theoretical reference to guide the parameter design of rockbolt reinforcement engineering in a circular symmetrical tunnel.

]]>Symmetry doi: 10.3390/sym10090380

Authors: Yongtao Li Xian-Ming Gu Jianxing Zhao

In the current note, we investigate the mathematical relations among the weighted arithmetic mean&ndash;geometric mean (AM&ndash;GM) inequality, the H&ouml;lder inequality and the weighted power-mean inequality. Meanwhile, the proofs of mathematical equivalence among the weighted AM&ndash;GM inequality, the weighted power-mean inequality and the H&ouml;lder inequality are fully achieved. The new results are more generalized than those of previous studies.

]]>Symmetry doi: 10.3390/sym10090379

Authors: Yong-An Jung Young-Hwan You

The integrated services digital broadcasting-terrestrial (ISDB-T) system is designed in order to accommodate high-quality video/audio and multimedia services, using band segmented transmission orthogonal frequency division multiplexing (BST-OFDM) scheme. In the ISDB-T system, the pilot configuration varies depending on whether a segment uses a coherent or differential modulation. Therefore, it is necessary to perform a joint estimation of carrier frequency offset (CFO) and sampling frequency offset (SFO) independent of the segment format in the ISDB-T system. The goal is to complete those synchronization tasks while considering an information-carrying transmission and multiplexing configuration control (TMCC) signal as pilot symbols. It is demonstrated through numerical simulations that the differential BPSK-modulated TMCC information can be efficiently used for a least-squares estimation of CFO and SFO, offering an acceptable performance.

]]>Symmetry doi: 10.3390/sym10090378

Authors: Temuer Chaolu Sudao Bilige

In this paper, we present an application of Wu&rsquo;s method (differential characteristic set (dchar-set) algorithm) for computing the symmetry of (partial) differential equations (PDEs) that provides a direct and systematic procedure to obtain the classical and nonclassical symmetry of the differential equations. The fundamental theory and subalgorithms used in the proposed algorithm consist of a different version of the Lie criterion for the classical symmetry of PDEs and the zero decomposition algorithm of a differential polynomial (d-pol) system (DPS). The version of the Lie criterion yields determining equations (DTEs) of symmetries of differential equations, even those including a nonsolvable equation. The decomposition algorithm is used to solve the DTEs by decomposing the zero set of the DPS associated with the DTEs into a union of a series of zero sets of dchar-sets of the system, which leads to simplification of the computations.

]]>Symmetry doi: 10.3390/sym10090377

Authors: Wenguang Yu Yujuan Huang Chaoran Cui

The absolute ruin insurance risk model is modified by including some valuable market economic information factors, such as credit interest, debit interest and dividend payments. Such information is especially important for insurance companies to control risks. We further assume that the insurance company is able to finance and continue to operate when its reserve is negative. We investigate the integro-differential equations for some interest actuarial diagnostics. We also provide numerical examples to explain the effects of relevant parameters on actuarial diagnostics.

]]>Symmetry doi: 10.3390/sym10090376

Authors: Guokai Zhang Xiao Liu Dandan Zhu Pengcheng He Lipeng Liang Ye Luo Jianwei Lu

Lung cancer mortality is currently the highest among all kinds of fatal cancers. With the help of computer-aided detection systems, a timely detection of malignant pulmonary nodule at early stage could improve the patient survival rate efficiently. However, the sizes of the pulmonary nodules are usually various, and it is more difficult to detect small diameter nodules. The traditional convolution neural network uses pooling layers to reduce the resolution progressively, but it hampers the network&rsquo;s ability to capture the tiny but vital features of the pulmonary nodules. To tackle this problem, we propose a novel 3D spatial pyramid dilated convolution network to classify the malignancy of the pulmonary nodules. Instead of using the pooling layers, we use 3D dilated convolution to learn the detailed characteristic information of the pulmonary nodules. Furthermore, we show that the fusion of multiple receptive fields from different dilated convolutions could further improve the classification performance of the model. Extensive experimental results demonstrate that our model achieves a better result with an accuracy of 88.6 % , which outperforms other state-of-the-art methods.

]]>Symmetry doi: 10.3390/sym10090375

Authors: Zhen He Hangen He

Nowadays, video surveillance has become ubiquitous with the quick development of artificial intelligence. Multi-object detection (MOD) is a key step in video surveillance and has been widely studied for a long time. The majority of existing MOD algorithms follow the &ldquo;divide and conquer&rdquo; pipeline and utilize popular machine learning techniques to optimize algorithm parameters. However, this pipeline is usually suboptimal since it decomposes the MOD task into several sub-tasks and does not optimize them jointly. In addition, the frequently used supervised learning methods rely on the labeled data which are scarce and expensive to obtain. Thus, we propose an end-to-end Unsupervised Multi-Object Detection framework for video surveillance, where a neural model learns to detect objects from each video frame by minimizing the image reconstruction error. Moreover, we propose a Memory-Based Recurrent Attention Network to ease detection and training. The proposed model was evaluated on both synthetic and real datasets, exhibiting its potential.

]]>Symmetry doi: 10.3390/sym10090373

Authors: Arindam Dey Le Hoang Son P. K. Kishore Kumar Ganeshsree Selvachandran Shio Gai Quek

The vague graph has found its importance as a closer approximation to real life situations. A review of the literature in this area reveals that the edge coloring problem for vague graphs has not been studied until now. Therefore, in this paper, we analyse the concept of vertex and edge coloring on simple vague graphs. Specifically, two new definitions for vague graphs related to the concept of the &lambda;-strong-adjacent and &zeta;-strong-incident of vague graphs are introduced. We consider the color classes to analyze the coloring on the vertices in vague graphs. The proposed method illustrates the concept of coloring on vague graphs, using the definition of color class, which depends only on the truth membership function. Applications of the proposal in solving practical problems related to traffic flow management and the selection of advertisement spots are mainly discussed.

]]>Symmetry doi: 10.3390/sym10090374

Authors: Chi-Hua Chen Eyhab Al-Masri Feng-Jang Hwang Despo Ktoridou Kuen-Rong Lo

This editorial introduces the special issue, entitled &ldquo;Applications of Internet of Things&rdquo;, of Symmetry. The topics covered in this issue fall under four main parts: (I) communication techniques and applications, (II) data science techniques and applications, (III) smart transportation, and (IV) smart homes. Four papers on sensing techniques and applications are included as follows: (1) &ldquo;Reliability of improved cooperative communication over wireless sensor networks&rdquo;, by Chen et al.; (2) &ldquo;User classification in crowdsourcing-based cooperative spectrum sensing&rdquo;, by Zhai and Wang; (3) &ldquo;IoT&rsquo;s tiny steps towards 5G: Telco&rsquo;s perspective&rdquo;, by Cero et al.; and (4) &ldquo;An Internet of things area coverage analyzer (ITHACA) for complex topographical scenarios&rdquo;, by Parada et al. One paper on data science techniques and applications is as follows: &ldquo;Internet of things: a scientometric review&rdquo;, by Ruiz-Rosero et al. Two papers on smart transportation are as follows: (1) &ldquo;An Internet of things approach for extracting featured data using an AIS database: an application based on the viewpoint of connected ships&rdquo;, by He et al.; and (2) &ldquo;The development of key technologies in applications of vessels connected to the Internet&rdquo;, by Tian et al. Two papers on smart home are as follows: (1) &ldquo;A novel approach based on time cluster for activity recognition of daily living in smart homes&rdquo;, by Liu et al.; and (2) &ldquo;IoT-based image recognition system for smart home-delivered meal services&rdquo;, by Tseng et al.

]]>Symmetry doi: 10.3390/sym10090372

Authors: Ivan de Martino

Decaying Dark Energy models modify the background evolution of the most common observables, such as the Hubble function, the luminosity distance and the Cosmic Microwave Background temperature&ndash;redshift scaling relation. We use the most recent observationally-determined datasets, including Supernovae Type Ia and Gamma Ray Bursts data, along with H ( z ) and Cosmic Microwave Background temperature versus z data and the reduced Cosmic Microwave Background parameters, to improve the previous constraints on these models. We perform a Monte Carlo Markov Chain analysis to constrain the parameter space, on the basis of two distinct methods. In view of the first method, the Hubble constant and the matter density are left to vary freely. In this case, our results are compatible with previous analyses associated with decaying Dark Energy models, as well as with the most recent description of the cosmological background. In view of the second method, we set the Hubble constant and the matter density to their best fit values obtained by the Planck satellite, reducing the parameter space to two dimensions, and improving the existent constraints on the model&rsquo;s parameters. Our results suggest that the accelerated expansion of the Universe is well described by the cosmological constant, and we argue that forthcoming observations will play a determinant role to constrain/rule out decaying Dark Energy.

]]>Symmetry doi: 10.3390/sym10090370

Authors: Zhen He Shaobing Gao Liang Xiao Daxue Liu Hangen He

Modelling the multimedia data such as text, images, or videos usually involves the analysis, prediction, or reconstruction of them. The recurrent neural network (RNN) is a powerful machine learning approach to modelling these data in a recursive way. As a variant, the long short-term memory (LSTM) extends the RNN with the ability to remember information for longer. Whilst one can increase the capacity of LSTM by widening or adding layers, additional parameters and runtime are usually required, which could make learning harder. We therefore propose a Tensor LSTM where the hidden states are tensorised as multidimensional arrays (tensors) and updated through a cross-layer convolution. As parameters are spatially shared within the tensor, we can efficiently widen the model without extra parameters by increasing the tensorised size; as deep computations of each time step are absorbed by temporal computations of the time series, we can implicitly deepen the model with little extra runtime by delaying the output. We show by experiments that our model is well-suited for various multimedia data modelling tasks, including text generation, text calculation, image classification, and video prediction.

]]>Symmetry doi: 10.3390/sym10090371

Authors: José Carlos R. Alcantud María José Muñoz Torrecillas

This paper first merges two noteworthy aspects of choice. On the one hand, soft sets and fuzzy soft sets are popular models that have been largely applied to decision making problems, such as real estate valuation, medical diagnosis (glaucoma, prostate cancer, etc.), data mining, or international trade. They provide crisp or fuzzy parameterized descriptions of the universe of alternatives. On the other hand, in many decisions, costs and benefits occur at different points in time. This brings about intertemporal choices, which may involve an indefinitely large number of periods. However, the literature does not provide a model, let alone a solution, to the intertemporal problem when the alternatives are described by (fuzzy) parameterizations. In this paper, we propose a novel soft set inspired model that applies to the intertemporal framework, hence it fills an important gap in the development of fuzzy soft set theory. An algorithm allows the selection of the optimal option in intertemporal choice problems with an infinite time horizon. We illustrate its application with a numerical example involving alternative portfolios of projects that a public administration may undertake. This allows us to establish a pioneering intertemporal model of choice in the framework of extended fuzzy set theories.

]]>Symmetry doi: 10.3390/sym10090369

Authors: Huawei Zhai Licheng Cui Yu Nie Xiaowei Xu Weishi Zhang

In order to meet the real-time public travel demands, the bus operators need to adjust the timetables in time. Therefore, it is necessary to predict the variations of the short-term passenger flow. Under the help of the advanced public transportation systems, a large amount of real-time data about passenger flow is collected from the automatic passenger counters, automatic fare collection systems, etc. Using these data, different kinds of methods are proposed to predict future variations of the short-term bus passenger flow. Based on the properties and background knowledge, these methods are classified into three categories: linear, nonlinear and combined methods. Their performances are evaluated in detail in the major aspects of the prediction accuracy, the complexity of training data structure and modeling process. For comparison, some long-term prediction methods are also analyzed simply. At last, it points that, with the help of automatic technology, a large amount of data about passenger flow will be collected, and using the big data technology to speed up the data preprocessing and modeling process may be one of the directions worthy of study in the future.

]]>Symmetry doi: 10.3390/sym10090368

Authors: Vasilis K. Oikonomou

In this paper, an experimental method that may reveal possible aggregate symmetrical structures in highly diluted solutions is proposed, generated by the method of the release activity, which is not yet completely proven. The release activity phenomenon (regardless of whether or not it is real) could be viewed as being quite controversial. However, the focus of this paper is to reveal any possible higher-order, pragmatic, underlying symmetry or structure supporting this theory, by proposing an experiment based on viscosity. Our proposal is based on the sequential measurement of the viscosity of a highly diluted solution and the perturbative expansion of the viscosity as a function of the concentration. The coefficients of this perturbative expansion directly quantify the modification of the hydrodynamic flow around particles and around higher-order structures. Any deviation from a linear dependence of the viscosity, as a function of the concentration, could potentially reveal a collective structure of some sort, or some symmetrical pattern in the solvent. We describe our experimental proposal for non-electrolyte solutes, and future directions for revealing collective structures in solutions are discussed as related to the release activity method. Regardless of whether or not the release activity is pragmatic, it needs to be scrutinized in order to reveal its inner workings. Finally, some theoretical arguments are presented to support the proposal.

]]>Symmetry doi: 10.3390/sym10090367

Authors: Donghai Liu Yuanyuan Liu Xiaohong Chen

The existing cosine similarity measure for hesitant fuzzy linguistic term sets (HFLTSs) has an impediment as it does not satisfy the axiom of similarity measure. Due to this disadvantage, a new similarity measure combining the existing cosine similarity measure and the Euclidean distance measure of HFLTSs is proposed, which is constructed based on a linguistic scale function; the related properties are also given. According to the relationship between the distance measure and the similarity measure, a corresponding distance measure between HFLTSs is obtained. Furthermore, we generalize the technique for order preference by similarity to an ideal solution (TOPSIS) method to the obtained distance measure of the HFLTSs. The principal advantages of the proposed method are that it cannot only effectively transform linguistic information in different semantic environments, but it can also avoid the shortcomings of existing the cosine similarity measure. Finally, a case study is conducted to illustrate the feasibility and effectiveness of the proposed method, which is compared to the existing methods.

]]>Symmetry doi: 10.3390/sym10090366

Authors: Pawel Gusin Andy Augousti Filip Formalik Andrzej Radosz

A black hole in a Schwarzschild spacetime is considered. A transformation is proposed that describes the relationship between the coordinate systems exterior and interior to an event horizon. The application of this transformation permits considerations of the (a)symmetry of a range of phenomena taking place on both sides of the event horizon. The paper investigates two distinct problems of a uniformly accelerated particle. In one of these, although the equations of motion are the same in the regions on both sides, the solutions turn out to be very different. This manifests the differences of the properties of these two ranges.

]]>Symmetry doi: 10.3390/sym10090365

Authors: Hamiyet Merkepçi

Mathematical physics looks for ways to apply mathematical ideas to problems in physics. In differential forms, the tensor form is first defined, and the definitions of exterior and symmetric differential forms are made accordingly. For instance, M is an R-module, M &otimes; R M the tensor product of M with itself and H a submodule of M &otimes; R M generated by x &otimes; y &minus; y &otimes; x , where x , y in M. Then, &or; 2 ( M ) = M &otimes; R M / H is called the second symmetric power of M. A role of the exterior differential forms in field theory is related to the conservation laws for physical fields, etc. In this study, I present a new approach to emphasize the properties of second exterior and symmetric derivations on Kahler modules, and I find a connection between them. I constitute exact sequences of &or; 2 ( &Omega; 1 ( S ) ) and &Lambda; 2 ( &Omega; 1 ( S ) ) , and I describe and prove a new isomorphism in the following: Let S be an affine algebra presented by R / I , where R = k [ x 1 , &hellip; x s ] is a polynomial algebra and I = ( f 1 , &hellip; f m ) an ideal of R. Then, I have J 1 &Omega; 1 ( S ) ≃ &Omega; 1 ( S ) &oplus; &or; 2 ( &Omega; 1 ( S ) ) &oplus; &Lambda; 2 ( &Omega; 1 ( S ) .

]]>Symmetry doi: 10.3390/sym10090364

Authors: Ru-xia Liang Zi-bin Jiang Jian-qiang Wang

Competition among different universities depends largely on the competition for talent. Talent evaluation and selection is one of the main activities in human resource management (HRM) which is critical for university development. Firstly, linguistic neutrosophic sets (LNSs) are introduced to better express multiple uncertain information during the evaluation procedure. We further merge the power averaging operator with LNSs for information aggregation and propose a LN-power weighted averaging (LNPWA) operator and a LN-power weighted geometric (LNPWG) operator. Then, an extended technique for order preference by similarity to ideal solution (TOPSIS) method is developed to solve a case of university HRM evaluation problem. The main contribution and novelty of the proposed method rely on that it allows the information provided by different decision makers (DMs) to support and reinforce each other which is more consistent with the actual situation of university HRM evaluation. In addition, its effectiveness and advantages over existing methods are verified through sensitivity and comparative analysis. The results show that the proposal is capable in the domain of university HRM evaluation and may contribute to the talent introduction in universities.

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Authors: G.C. Yang Z.Y. Li

We study one-dimensional p-Laplacian problems and answer the unsolved problem. Our method is to study the property of the operator, the concavity of the solutions and the continuity of the first eigenvalues. By the above study, the main difficulty is overcome and the fixed point theorem can be applied for the corresponding compact maps. An affirmative answer is given to the unsolved problem with superlinearity. A global growth condition is not imposed on the nonlinear term f. The assumptions of this paper are more general than the usual, thus the existing results cannot be utilized. Some recent results are improved from weak solutions to classical solutions and from p ≥ 2 to p ∈ ( 1 , ∞ ) .

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Authors: Gaoshen Cai Chuanyu Wu Dongxing Zhang

The warm sheet cylindrical deep drawing experiment of aluminum alloy was carried out and macro-mechanical properties and microstructure evolution of hydro-formed cups with different cooling medium were analyzed, which aimed to investigate the effects of different types of cooling on mechanical properties and microstructure of cylindrical cups hydro-formed by warm Hydro-mechanical Deep Drawing (HDD). Results show that, under the condition of warm hydroforming, the mechanical properties such as yield stress and ultimate strength were influenced very little by air or water cooling. Grain coarsening of these hydro-formed cups can be inhibited to a certain extent with subsequent rapid water cooling. Moreover, it shows that the processing with warm sheet hydroforming and subsequent rapid cooling of 7075-O aluminum alloy has a positive significance in maintaining the stability of macro mechanical properties and inhibiting the degradation of the microstructure of materials.

]]>Symmetry doi: 10.3390/sym10090361

Authors: Rita Ambu Anna Eva Morabito

In tissue engineering, biocompatible porous scaffolds that try to mimic the features and function of the bone are of great relevance. In this paper, an effective method for the design of 3D porous scaffolds is applied to the modelling of structures with variable architectures. These structures are of interest since they are more similar to the stochastic configuration of real bone with respect to architectures made of a unit cell replicated in three orthogonal directions, which are usually considered for this kind of applications. This property configures them as, potentially, more suitable to satisfy simultaneously the biological requirements and those relative to the mechanical strength. The procedure implemented is based on the implicit surface modelling method and the use of a triply periodic minimal surface (TPMS), specifically, the Schwarz&rsquo;s Primitive (P) minimal surface, whose geometry was considered for the development of scaffolds with different configurations. The representative structures modelled were numerically analysed by means of finite element analysis (FEA), considering them made of a biocompatible titanium alloy. The architectures considered were thus assessed in terms of the relationship between the geometrical configuration and the mechanical response to compression loading.

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Authors: J. A. Méndez-Bermúdez Rosalío Reyes José M. Rodríguez José M. Sigarreta

A graph operator is a mapping F : &Gamma; &rarr; &Gamma; &prime; , where &Gamma; and &Gamma; &prime; are families of graphs. The different kinds of graph operators are an important topic in Discrete Mathematics and its applications. The symmetry of this operations allows us to prove inequalities relating the hyperbolicity constants of a graph G and its graph operators: line graph, &Lambda; ( G ) ; subdivision graph, S ( G ) ; total graph, T ( G ) ; and the operators R ( G ) and Q ( G ) . In particular, we get relationships such as &delta; ( G ) &le; &delta; ( R ( G ) ) &le; &delta; ( G ) + 1 / 2 , &delta; ( &Lambda; ( G ) ) &le; &delta; ( Q ( G ) ) &le; &delta; ( &Lambda; ( G ) ) + 1 / 2 , &delta; ( S ( G ) ) &le; 2 &delta; ( R ( G ) ) &le; &delta; ( S ( G ) ) + 1 and &delta; ( R ( G ) ) &minus; 1 / 2 &le; &delta; ( &Lambda; ( G ) ) &le; 5 &delta; ( R ( G ) ) + 5 / 2 for every graph which is not a tree. Moreover, we also derive some inequalities for the Gromov product and the Gromov product restricted to vertices.

]]>Symmetry doi: 10.3390/sym10090359

Authors: Wenpeng Zhang Xin Lin

The aim of this paper is to study the congruence properties of a new sequence, which is closely related to Fubini polynomials and Euler numbers, using the elementary method and the properties of the second kind Stirling numbers. As results, we obtain some interesting congruences for it. This solves a problem proposed in a published paper.

]]>Symmetry doi: 10.3390/sym10090358

Authors: Chen Yang

In this work, a three-point boundary value problem of fractional q-difference equations is discussed. By using fixed point theorems on mixed monotone operators, some sufficient conditions that guarantee the existence and uniqueness of positive solutions are given. In addition, an iterative scheme can be made to approximate the unique solution. Finally, some interesting examples are provided to illustrate the main results.

]]>Symmetry doi: 10.3390/sym10090357

Authors: Zhen Tan Bo Li Peixin Huang Bin Ge Weidong Xiao

Relation classification (RC) is an important task in information extraction from unstructured text. Recently, several neural methods based on various network architectures have been adopted for the task of RC. Among them, convolution neural network (CNN)-based models stand out due to their simple structure, low model complexity and &ldquo;good&rdquo; performance. Nevertheless, there are still at least two limitations associated with existing CNN-based RC models. First, when handling samples with long distances between entities, they fail to extract effective features, even obtaining disturbing ones from the clauses, which results in decreased accuracy. Second, existing RC models tend to produce inconsistent results when fed with forward and backward instances of an identical sample. Therefore, we present a novel CNN-based sentence encoder with selective attention by leveraging the shortest dependency paths, and devise a classification framework using symmetrical directional&mdash;forward and backward&mdash;instances via information fusion. Comprehensive experiments verify the superior performance of the proposed RC model over mainstream competitors without additional artificial features.

]]>Symmetry doi: 10.3390/sym10090356

Authors: Jose A. Diaz-Severiano Valentin Gomez-Jauregui Cristina Manchado Cesar Otero

This paper shows a methodology for reducing the complex design process of space structures to an adequate selection of points lying on a plane. This procedure can be directly implemented in a bi-dimensional plane when we substitute (i) Euclidean geometry by bi-dimensional projection of the elliptic geometry and (ii) rotations/symmetries on the sphere by M&ouml;bius transformations on the plane. These graphs can be obtained by sites, specific points obtained by homological transformations in the inversive plane, following the analogous procedure defined previously in the three-dimensional space. From the sites, it is possible to obtain different partitions of the plane, namely, power diagrams, Voronoi diagrams, or Delaunay triangulations. The first would generate geo-tangent structures on the sphere; the second, panel structures; and the third, lattice structures.

]]>Symmetry doi: 10.3390/sym10090355

Authors: Hong-Kun Lyu Chi-Ho Park Dong-Hee Han Seong Woo Kwak Byeongdae Choi

In the case of autonomous orchard navigation, researchers have developed algorithms that utilize features, such as trunks, canopies, and sky in orchards, but there are still various difficulties in recognizing free space for autonomous navigation in a changing agricultural environment. In this study, we applied the Naive Bayesian classification to detect the boundary between the trunk and the ground and propose an algorithm to determine the center line of free space. The na&iuml;ve Bayesian classification requires a small number of samples for training and a simple training process. In addition, it was able to effectively classify tree trunk&rsquo;s points and noise points of the orchard, which are problematic in vision-based processing, and noise caused by small branches, soil, weeds, and tree shadows on the ground. The performance of the proposed algorithm was investigated using 229 sample images obtained from an image acquisition system with a Complementary Metal Oxide Semiconductor (CMOS) Image Sensor (CIS) camera. The center line detected by the unaided-eye manual decision and the results extracted by the proposed algorithm were compared and analyzed for several parameters. In all compared parameters, extracted center line was more stable than the manual center line results.

]]>Symmetry doi: 10.3390/sym10080354

Authors: Tomasz Czyżycki Jiří Hrivnák Jiří Patera

The generating functions of fourteen families of generalized Chebyshev polynomials related to rank two Lie algebras A 2 , C 2 and G 2 are explicitly developed. There exist two classes of the orthogonal polynomials corresponding to the symmetric and antisymmetric orbit functions of each rank two algebra. The Lie algebras G 2 and C 2 admit two additional polynomial collections arising from their hybrid character functions. The admissible shift of the weight lattice permits the construction of a further four shifted polynomial classes of C 2 and directly generalizes formation of the classical univariate Chebyshev polynomials of the third and fourth kinds. Explicit evaluating formulas for each polynomial family are derived and linked to the incomplete exponential Bell polynomials.

]]>Symmetry doi: 10.3390/sym10080353

Authors: Tran Song Dat Phuc Changhoon Lee

BM123-64 block cipher, which was proposed by Minh, N.H. and Bac, D.T. in 2014, was designed for high speed communication applications factors. It was constructed in hybrid controlled substitution&ndash;permutation network (CSPN) models with two types of basic controlled elements (CE) in distinctive designs. This cipher is based on switchable data-dependent operations (SDDO) and covers dependent-operations suitable for efficient primitive approaches for cipher constructions that can generate key schedule in a simple way. The BM123-64 cipher has advantages including high applicability, flexibility, and portability with different algorithm selection for various application targets with internet of things (IoT) as well as secure protection against common types of attacks, for instance, differential attacks and linear attacks. However, in this paper, we propose methods to possibly exploit the BM123-64 structure using related-key attacks. We have constructed a high probability related-key differential characteristics (DCs) on a full eight rounds of BM123-64 cipher. The related-key amplified boomerang attack is then proposed on all three different cases of operation-specific designs with effective results in complexity of data and time consumptions. This study can be considered as the first cryptographic results on BM123-64 cipher.

]]>Symmetry doi: 10.3390/sym10080352

Authors: An Braeken

Key agreement between two constrained Internet of Things (IoT) devices that have not met each other is an essential feature to provide in order to establish trust among its users. Physical Unclonable Functions (PUFs) on a device represent a low cost primitive exploiting the unique random patterns in the device and have been already applied in a multitude of applications for secure key generation and key agreement in order to avoid an attacker to take over the identity of a tampered device, whose key material has been extracted. This paper shows that the key agreement scheme of a recently proposed PUF based protocol, presented by Chatterjee et al., for Internet of Things (IoT) is vulnerable for man-in-the-middle, impersonation, and replay attacks in the Yao&ndash;Dolev security model. We propose an alternative scheme, which is able to solve these issues and can provide in addition a more efficient key agreement and subsequently a communication phase between two IoT devices connected to the same authentication server. The scheme also offers identity based authentication and repudiation, when only using elliptic curve multiplications and additions, instead of the compute intensive pairing operations.

]]>Symmetry doi: 10.3390/sym10080351

Authors: José Ignacio Rojas-Sola Belén Galán-Moral Eduardo De la Morena-De la Fuente

In this paper, the geometric modeling and virtual reconstruction of the double-acting steam engine designed by Agust&iacute;n de Betancourt in 1789 are shown. For this, the software Autodesk Inventor Professional is used, which has allowed us to obtain its geometric documentation. The material for the research is available on the website of the Betancourt Project of the Canary Orotava Foundation for the History of Science. Almost all parts of the steam engine are drawn on the sheets, but due to the absence of scale and space, it is insufficient to obtain an accurate and reliable 3D CAD (Computer-Aided Design) model. For this reason a graphic scale has been adopted so that the dimensions of the elements are coherent. Also, it has been necessary to make some dimensional and geometric hypotheses, as well as restrictions of movement (degrees of freedom). Geometric modeling has made it possible to know that the system is balanced with the geometric center of the rocker arm shaft, and presents an energetic symmetry whose axis is the support of the parallelogram where the shaft rests: calorific energy to the left and mechanical energy to the right, with the rocker arm acting as a transforming element from one to the other.

]]>Symmetry doi: 10.3390/sym10080350

Authors: Rajab Ali Borzooei Xiaohong Zhang Florentin Smarandache Young Bae Jun

The concept of a commutative generalized neutrosophic ideal in a B C K -algebra is proposed, and related properties are proved. Characterizations of a commutative generalized neutrosophic ideal are considered. Also, some equivalence relations on the family of all commutative generalized neutrosophic ideals in B C K -algebras are introduced, and some properties are investigated.

]]>Symmetry doi: 10.3390/sym10080349

Authors: Jianping Wu Boliang Lin Hui Wang Xuhui Zhang Zhongkai Wang Jiaxi Wang

Electric multiple unit (EMU) trains&rsquo; high-level maintenance planning is a discrete problem in mathematics. The high-level maintenance process of the EMU trains consumes plenty of time. When the process is undertaken during peak periods of the passenger flow, the transportation demand may not be fully satisfied due to the insufficient supply of trains. In contrast, if the process is undergone in advance, extra costs will be incurred. Based on the practical requirements of high-level maintenance, a 0&ndash;1 programming model is proposed. To simplify the description of the model, candidate sets of delivery dates, i.e., time windows, are generated according to the historical data and maintenance regulations. The constraints of the model include maintenance regulations, the passenger transportation demand, and capacities of workshop. The objective function is to minimize the mileage losses of all EMU trains. Moreover, a modified particle swarm algorithm is developed for solving the problem. Finally, a real-world case study of Shanghai Railway is conducted to demonstrate the proposed method. Computational results indicate that the (approximate) optimal solution can be obtained successfully by our method and the proposed method significantly reduces the solution time to 500 s.

]]>Symmetry doi: 10.3390/sym10080348

Authors: Nak Eun Cho Virendra Kumar V. Ravichandran

Higher order Schwarzian derivatives for normalized univalent functions were first considered by Schippers, and those of convex functions were considered by Dorff and Szynal. In the present investigation, higher order Schwarzian derivatives for the Janowski star-like and convex functions are considered, and sharp bounds for the first three consecutive derivatives are investigated. The results obtained in this paper generalize several existing results in this direction.

]]>Symmetry doi: 10.3390/sym10080347

Authors: Mohanad Aljanabi Yasa Ekşioğlu Özok Javad Rahebi Ahmad S. Abdullah

The occurrence rates of melanoma are rising rapidly, which are resulting in higher death rates. However, if the melanoma is diagnosed in Phase I, the survival rates increase. The segmentation of the melanoma is one of the largest tasks to undertake and achieve when considering both beneath and over the segmentation. In this work, a new approach based on the artificial bee colony (ABC) algorithm is proposed for the detection of melanoma from digital images. This method is simple, fast, flexible, and requires fewer parameters compared with other algorithms. The proposed approach is applied on the PH2, ISBI 2016 challenge, the ISBI 2017 challenge, and Dermis datasets. These bases contained images are affected by different abnormalities. The formation of the databases consists of images collected from different sources; they are bases with different types of resolution, lighting, etc., so in the first step, the noise was removed from the images by using morphological filtering. In the next step, the ABC algorithm is used to find the optimum threshold value for the melanoma detection. The proposed approach achieved good results in the conditions of high specificity. The experimental results suggest that the proposed method accomplished higher performance compared to the ground truth images supported by a Dermatologist. For the melanoma detection, the method achieved an average accuracy and Jaccard&rsquo;s coefficient in the range of 95.24&ndash;97.61%, and 83.56&ndash;85.25% in these four databases. To show the robustness of this work, the results were compared to existing methods in the literature for melanoma detection. High values for estimation performance confirmed that the proposed melanoma detection is better than other algorithms, which demonstrates the highly differential power of the newly introduced features.

]]>Symmetry doi: 10.3390/sym10080346

Authors: Wen Jiang Yu Zhong Xinyang Deng

Fault diagnosis is an important issue in various fields and aims to detect and identify the faults of systems, products, and processes. The cause of a fault is complicated due to the uncertainty of the actual environment. Nevertheless, it is difficult to consider uncertain factors adequately with many traditional methods. In addition, the same fault may show multiple features and the same feature might be caused by different faults. In this paper, a neutrosophic set based fault diagnosis method based on multi-stage fault template data is proposed to solve this problem. For an unknown fault sample whose fault type is unknown and needs to be diagnosed, the neutrosophic set based on multi-stage fault template data is generated, and then the generated neutrosophic set is fused via the simplified neutrosophic weighted averaging (SNWA) operator. Afterwards, the fault diagnosis results can be determined by the application of defuzzification method for a defuzzying neutrosophic set. Most kinds of uncertain problems in the process of fault diagnosis, including uncertain information and inconsistent information, could be handled well with the integration of multi-stage fault template data and the neutrosophic set. Finally, the practicality and effectiveness of the proposed method are demonstrated via an illustrative example.

]]>Symmetry doi: 10.3390/sym10080345

Authors: Vasantha Kandasamy W.B. Ilanthenral Kandasamy Florentin Smarandache

The notions of neutrosophy, neutrosophic algebraic structures, neutrosophic duplet and neutrosophic triplet were introduced by Florentin Smarandache. In this paper, the neutrosophic duplets of Z p n , Z p q and Z p 1 p 2 &hellip; p n are studied. In the case of Z p n and Z p q , the complete characterization of neutrosophic duplets are given. In the case of Z p 1 &hellip; p n , only the neutrosophic duplets associated with p i s are provided; i = 1 , 2 , &hellip; , n . Some open problems related to neutrosophic duplets are proposed.

]]>Symmetry doi: 10.3390/sym10080344

Authors: Vijai Jayadevan Tadamasa Sawada Edward Delp Zygmunt Pizlo

The human visual system uses priors to convert an ill-posed inverse problem of 3D shape recovery into a well-posed one. In previous studies, we have demonstrated the use of priors like symmetry, compactness and minimal surface in the perception of 3D symmetric shapes. We also showed that binocular perception of symmetric shapes can be well modeled by the above-mentioned priors and binocular depth order information. In this study, which used a shape-matching task, we show that these priors can also be used to model perception of near-symmetrical shapes. Our near-symmetrical shapes are asymmetrical shapes obtained from affine distortions of symmetrical shapes. We found that the perception of symmetrical shapes is closer to veridical than the perception of asymmetrical shapes. We introduce a metric to measure asymmetry of abstract polyhedral shapes, and a similar metric to measure shape dissimilarity between two polyhedral shapes. We report some key observations obtained by analyzing the data from the experiment. A website was developed with all the shapes used in the experiment, along with the shapes recovered by the subject and the shapes recovered by the model. This website provides a qualitative analysis of the effectiveness of the model and also helps demonstrate the goodness of the shape metric.

]]>Symmetry doi: 10.3390/sym10080343

Authors: Stefan Yoshi Buhmann A. Salam

Non-pairwise additive three-body dispersion potentials dependent upon one or more electric octupole moments are evaluated using the theory of molecular quantum electrodynamics. To simplify the perturbation theory calculations, an effective two-photon interaction Hamiltonian operator is employed. This leads to only third-order theory being required to evaluate energy shifts instead of the usual sixth-order formula, and the summation over six time-ordered sequences of virtual photon creation and annihilation events. Specific energy shifts computed include DD-DD-DO, DD-DO-DO, DO-DO-DO, and DD-DO-OO terms, where D and O are electric dipole and octupole moments, respectively. The formulae obtained are applicable to an arbitrary arrangement of the three particles, and we present explicit results for the equilateral triangle and collinear configurations, which complements the recently published DD-DD-OO potential. In this last case it was found that the contribution from the octupole weight-1 term could be viewed as a higher-order correction to the triple-dipole dispersion potential DD-DD-DD. In a similar fashion the octupole moment is decomposed into its irreducible components of weights-1 and -3, enabling insight to be gained into the potentials obtained in this study. Dispersion interaction energies proportional to mixed dipole-octupole polarisabilities, for example, are found to depend only on the weight-1 octupole moment for isotropic species and are retarded. Additional approximations are necessary in the evaluation of wave vector integrals for these cases in order to yield energy shifts that are valid in the near-zone.

]]>Symmetry doi: 10.3390/sym10080342

Authors: Behrooz Hosseini Kourosh Kiani

Unsupervised machine learning and knowledge discovery from large-scale datasets have recently attracted a lot of research interest. The present paper proposes a distributed big data clustering approach-based on adaptive density estimation. The proposed method is developed-based on Apache Spark framework and tested on some of the prevalent datasets. In the first step of this algorithm, the input data is divided into partitions using a Bayesian type of Locality Sensitive Hashing (LSH). Partitioning makes the processing fully parallel and much simpler by avoiding unneeded calculations. Each of the proposed algorithm steps is completely independent of the others and no serial bottleneck exists all over the clustering procedure. Locality preservation also filters out the outliers and enhances the robustness of the proposed approach. Density is defined on the basis of Ordered Weighted Averaging (OWA) distance which makes clusters more homogenous. According to the density of each node, the local density peaks will be detected adaptively. By merging the local peaks, final cluster centers will be obtained and other data points will be a member of the cluster with the nearest center. The proposed method has been implemented and compared with similar recently published researches. Cluster validity indexes achieved from the proposed method shows its superiorities in precision and noise robustness in comparison with recent researches. Comparison with similar approaches also shows superiorities of the proposed method in scalability, high performance, and low computation cost. The proposed method is a general clustering approach and it has been used in gene expression clustering as a sample of its application.

]]>Symmetry doi: 10.3390/sym10080341

Authors: Aliyu Isa Aliyu Mustafa Inc Abdullahi Yusuf Dumitru Baleanu

In this work, we study the completely integrable sixth-order nonlinear Ramani equation. By applying the Lie symmetry analysis technique, the Lie point symmetries and the optimal system of one-dimensional sub-algebras of the equation are derived. The optimal system is further used to derive the symmetry reductions and exact solutions. In conjunction with the Riccati Bernoulli sub-ODE (RBSO), we construct the travelling wave solutions of the equation by solving the ordinary differential equations (ODEs) obtained from the symmetry reduction. We show that the equation is nonlinearly self-adjoint and construct the conservation laws (CL) associated with the Lie symmetries by invoking the conservation theorem due to Ibragimov. Some figures are shown to show the physical interpretations of the acquired results.

]]>Symmetry doi: 10.3390/sym10080340

Authors: Jinrui Chen Kesheng Liu Xuehu Yan Lintao Liu Xuan Zhou Longdan Tan

Secret image sharing (SIS) with small-sized shadow images has many benefits, such as saving storage space, improving transmission time, and achieving information hiding. When adjacent pixel values in an image are similar to each other, the secret image will be leaked when all random factors of an SIS scheme are utilized for achieving small sizes of shadow images. Most of the studies in this area suffer from an inevitable problem: auxiliary encryption is crucial in ensuring the security of those schemes. In this paper, an SIS scheme with small-sized shadow images based on the Chinese remainder theorem (CRT) is proposed. The size of shadow images can be reduced to nearly 1 / k of the original secret image. By adding random bits to binary representations of the random factors in the CRT, auxiliary encryption is not necessary for this scheme. Additionally, reasonable modifications of the random factors make it possible to incorporate all advantages of the CRT as well, including a ( k , n ) threshold, lossless recovery, and low computation complexity. Analyses and experiments are provided to demonstrate the effectiveness of the proposed scheme.

]]>Symmetry doi: 10.3390/sym10080339

Authors: Yi-Fang Chen Hui-Chin Tang

We consider the constrained ordered weighted averaging (OWA) aggregation problem with a single constraint and lower bounded variables. For the three-dimensional constrained OWA aggregation problem with lower bounded variables, we present four types of solution depending on the number of zero elements. According to the computerized experiment we perform, the lower bounds can affect the solution types, thereby affecting the optimal solution of the three-dimensional constrained OWA aggregation problem with lower bounded variables.

]]>Symmetry doi: 10.3390/sym10080338

Authors: Kanghuai Liu Zhigang Chen Jia Wu Leilei Wang

At the dawn of big data and 5G networks, end-to-end communication with large amounts of data between mobile devices is difficult to be implemented through the traditional face-to-face transmission mechanism in social networks. Consequently, opportunistic social networks proposed that message applications should choose proper relay nodes to perform effective data transmission processes. At present, several routing algorithms, based on node similarity, attempt to use the contextual information related to nodes and the special relationships between them to select a suitable relay node among neighbors. However, when evaluating the similarity degree between a pair of nodes, most existing algorithms in opportunistic social networks pay attention to only a few similar factors, and even ignore the importance of mobile similarity in the data transmission process. To improve the transmission environment, this study establishes a fuzzy routing-forwarding algorithm (FCNS) exploiting comprehensive node similarity (the mobile and social similarities) in opportunistic social networks. In our proposed scheme, the transmission preference of the node is determined through the fuzzy evaluation of mobile and social similarities. The suitable message delivery decision is made by collecting and comparing the transmission preference of nodes, and the sustainable and stable data transmission process is performed through the feedback mechanism. Through simulations and the comparison of social network algorithms, the delivery ratio in the proposed algorithm is 0.85 on average, and the routing delay and network overhead of this algorithm are always the lowest.

]]>Symmetry doi: 10.3390/sym10080337

Authors: Chui-Yu Chiu Po-Chou Shih Xuechao Li

A novel global harmony search (NGHS) algorithm, as proposed in 2010, is an improved algorithm that combines the harmony search (HS), particle swarm optimization (PSO), and a genetic algorithm (GA). Moreover, the fixed parameter of mutation probability was used in the NGHS algorithm. However, appropriate parameters can enhance the searching ability of a metaheuristic algorithm, and their importance has been described in many studies. Inspired by the adjustment strategy of the improved harmony search (IHS) algorithm, a dynamic adjusting novel global harmony search (DANGHS) algorithm, which combines NGHS and dynamic adjustment strategies for genetic mutation probability, is introduced in this paper. Moreover, extensive computational experiments and comparisons are carried out for 14 benchmark continuous optimization problems. The results show that the proposed DANGHS algorithm has better performance in comparison with other HS algorithms in most problems. In addition, the proposed algorithm is more efficient than previous methods. Finally, different strategies are suitable for different situations. Among these strategies, the most interesting and exciting strategy is the periodic dynamic adjustment strategy. For a specific problem, the periodic dynamic adjustment strategy could have better performance in comparison with other decreasing or increasing strategies. These results inspire us to further investigate this kind of periodic dynamic adjustment strategy in future experiments.

]]>Symmetry doi: 10.3390/sym10080336

Authors: Jie Liu Hui Tian Chin-Chen Chang Tian Wang Yonghong Chen Yiqiao Cai

This paper concentrates on the detection of steganography in inactive frames of low bit rate audio streams in Voice over Internet Protocol (VoIP) scenarios. Both theoretical and experimental analyses demonstrate that the distribution of 0 and 1 in encoding parameter bits becomes symmetric after a steganographic process. Moreover, this symmetry affects the frequency of each subsequence of parameter bits, and accordingly changes the poker test statistical features of encoding parameter bits. Employing the poker test statistics of each type of encoding parameter bits as detection features, we present a steganalysis method based on a support vector machine. We evaluate the proposed method with a large quantity of speech samples encoded by G.723.1 and compare it with the entropy test. The experimental results show that the proposed method is effective, and largely outperforms the entropy test in any cases.

]]>Symmetry doi: 10.3390/sym10080335

Authors: J. A. López-Campos A. Segade E. Casarejos J. R. Fernández J. A. Vilán P. Izquierdo

This paper studies the stress state of a threaded fastening by using Finite Element (FE) models, applied to surgical screws in cortical bone. There is a general interest in studying the stress states induced in the different elements of a joint caused by the thread contact. Analytical models were an initial approach, and later FE models allowed detailed studies of the complex phenomena related to these joints. Different studies have evaluated standard threaded joints in machinery and structures, being the thread symmetric. However, surgical screws employ asymmetric thread geometry, selected to improve the stress level generated in the bone. Despite the interest and widespread use, there is scarce documentation on the actual effect of this thread type. In this work, we discuss the results provided by FE models with detailed descriptions of the contacts comparing differences caused by the materials of the joint, the thread geometry and the thread&rsquo;s three-dimensional helical effects. The complex contacts at the threaded surfaces cause intense demand on computational resources that often limits the studies including these joints. We analyze the results provided by one commercial software package to simplify the threaded joints. The comparison with detailed FE models allows a definition of the level of uncertainty and possible limitations of this type of simplifications, and helps in making suitable choices for complex applications.

]]>Symmetry doi: 10.3390/sym10080334

Authors: Francesco Naddeo Alessandro Naddeo Nicola Cappetti Emilio Cataldo Riccardo Militio

In this article, the authors propose a novel procedure for designing a customized 3D-printed surgical template to guide surgeons in inserting screws into the sacral zone during arthrodesis surgeries. The template is characterized by two cylindrical guides defined by means of trajectories identified, based on standard procedure, via an appropriate Computer-Aided-Design (CAD)-based procedure. The procedure is based on the definition of the insertion direction by means of anatomical landmarks that enable the screws to take advantage of the maximum available bone path. After 3D printing, the template adheres perfectly to the bone surface, showing univocal positioning by exploiting the foramina of the sacrum, great maneuverability due to the presence of an ergonomic handle, as well as a break system for the two independent guides. These features make the product innovative. Thanks to its small size and the easy anchoring, the surgeon can simply position the template on the insertion area and directly insert the screws, without alterations to standard surgical procedures. This has the effect of reducing the overall duration of the surgery and the patient&rsquo;s exposure to X-rays, and increasing both the safety of the intervention and the quality of the results.

]]>Symmetry doi: 10.3390/sym10080333

Authors: Jinyan Wang Guoqing Cai Chen Liu Jingli Wu Xianxian Li

Nowadays, more and more applications are dependent on storage and management of semi-structured information. For scientific research and knowledge-based decision-making, such data often needs to be published, e.g., medical data is released to implement a computer-assisted clinical decision support system. Since this data contains individuals’ privacy, they must be appropriately anonymized before to be released. However, the existing anonymization method based on l-diversity for hierarchical data may cause serious similarity attacks, and cannot protect data privacy very well. In this paper, we utilize fuzzy sets to divide levels for sensitive numerical and categorical attribute values uniformly (a categorical attribute value can be converted into a numerical attribute value according to its frequency of occurrences), and then transform the value levels to sensitivity levels. The privacy model ( α l e v h , k)-anonymity for hierarchical data with multi-level sensitivity is proposed. Furthermore, we design a privacy-preserving approach to achieve this privacy model. Experiment results demonstrate that our approach is obviously superior to existing anonymous approach in hierarchical data in terms of utility and security.

]]>Symmetry doi: 10.3390/sym10080332

Authors: Muhammad Fazil Muhammad Murtaza Zafar Ullah Usman Ali Imran Javaid

Let G 1 and G 2 be disjoint copies of a graph G and g : V ( G 1 ) &rarr; V ( G 2 ) be a function. A functigraph F G consists of the vertex set V ( G 1 ) &cup; V ( G 2 ) and the edge set E ( G 1 ) &cup; E ( G 2 ) &cup; { u v : g ( u ) = v } . In this paper, we extend the study of distinguishing numbers of a graph to its functigraph. We discuss the behavior of distinguishing number in passing from G to F G and find its sharp lower and upper bounds. We also discuss the distinguishing number of functigraphs of complete graphs and join graphs.

]]>Symmetry doi: 10.3390/sym10080331

Authors: Raja Muhammad Hashim Muhammad Gulistan Florentin Smarandache

In this paper we provide an application of neutrosophic bipolar fuzzy sets in daily life&rsquo;s problem related with HOPE foundation that is planning to build a children hospital, which is the main theme of this paper. For it we first develop the theory of neutrosophic bipolar fuzzy sets which is a generalization of bipolar fuzzy sets. After giving the definition we introduce some basic operation of neutrosophic bipolar fuzzy sets and focus on weighted aggregation operators in terms of neutrosophic bipolar fuzzy sets. We define neutrosophic bipolar fuzzy weighted averaging ( N B FWA ) and neutrosophic bipolar fuzzy ordered weighted averaging ( N B FOWA ) operators. Next we introduce different kinds of similarity measures of neutrosophic bipolar fuzzy sets. Finally as an application we give an algorithm for the multiple attribute decision making problems under the neutrosophic bipolar fuzzy environment by using the different kinds of neutrosophic bipolar fuzzy weighted/fuzzy ordered weighted aggregation operators with a numerical example related with HOPE foundation.

]]>Symmetry doi: 10.3390/sym10080330

Authors: Wenhua Cui Jun Ye

Linguistic neutrosophic numbers (LNNs) are a powerful tool for describing fuzzy information with three independent linguistic variables (LVs), which express the degrees of truth, uncertainty, and falsity, respectively. However, existing LNNs cannot depict the hesitancy of the decision-maker (DM). To solve this issue, this paper first defines a hesitant linguistic neutrosophic number (HLNN), which consists of a few LNNs regarding an evaluated object due to DMs&rsquo; hesitancy to represent their hesitant and uncertain information in the decision-making process. Then, based on the least common multiple cardinality (LCMC), we present generalized distance and similarity measures of HLNNs, and then develop a similarity measure-based multiple-attribute decision-making (MADM) method to handle the MADM problem in the HLNN setting. Finally, the feasibility of the proposed approach is verified by an investment decision case.

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