Axioms doi: 10.3390/axioms11100517

Authors: Yongming Song

This paper proposes an interactive consensus reaching model in the group decision making for heterogeneous hesitant preference relations (i.e., hesitant fuzzy preference relations, hesitant multiplicative preference relations, hesitant fuzzy linguistic preference relations). First, the consistencies of three hesitant preference relations are defined, respectively. Then, based on their definitions, three optimization models are constructed to obtain the weight vector of alternatives, based on which an interactive consensus adjustment algorithm is established based on the direct consensus framework. This framework adopts feedback mechanism to facilitate the information correction of decision makers. After several rounds of adjustment, the decision results with satisfactory consensus level are achieved. Finally, the practicability and effectiveness of the model are illustrated through a case study of mine accident emergency decision making.

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Authors: Anum Shafiq Tabassum Naz Sindhu Showkat Ahmad Lone Marwa K. H. Hassan Kamsing Nonlaopon

In this paper, we propose a two-component mixture of Akash model (TC-MAM). The behavior of TC-MAM distribution has been presented graphically. Moment-based measures, including skewness, index of dispersion, kurtosis, and coefficient of variation, have been determined and hazard rate functions are presented graphically. The probability generating function, Mills ratio, characteristic function, cumulants, mean time to failure, and factorial moment generating function are all statistical aspects of the mixed model that we explore. Furthermore, we figure out the relevant parameters of the mixture model using the most suitable methods, such as least square, weighted least square, and maximum likelihood mechanisms. Findings of simulation experiments to examine behavior of these estimates are graphically presented. Finally, a set of data taken from the real world is examined in order to demonstrate the new model&rsquo;s practical perspectives. All of the metrics evaluated favor the new model and the superiority of proposed distribution over mixture of Lindley, Shanker, and exponential distributions.

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Authors: Fernando Castelló-Sirvent Carlos Meneses-Eraso

Systemic disruptions are becoming more continuous, intense, and persistent. Their effects have a severe impact on the economy in volatile, uncertain, complex, and ambiguous (VUCA) environments that are increasingly transversal to productive sectors and activities. Researchers have intensified their academic production of multiple-criteria decision-making (MCDM) in recent years. This article analyzes the research agenda through a systematic review of scientific articles in the Web of Science Core Collection according to the Journal Citation Report (JCR), both in the Social Sciences Citation Index (SSCI) and in the Science Citation Index Expanded (SCIE). According to the selected search criteria, 909 articles on MCDM published between 1979 and 2022 in Web of Science journals in the business and management categories were located. A bibliometric analysis of the main thematic clusters, the international collaboration networks, and the bibliographic coupling of articles was carried out. In addition, the analysis period is divided into two subperiods (1979&ndash;2008 and 2009&ndash;2022), establishing 2008 as the threshold, the year of the Global Financial Crisis (GFC), to assess the evolution of the research agenda at the beginning of systemic disruptions. The bibliometric analysis allows the identification of the motor, basic, specialized, and emerging themes of each subperiod. The results show the similarities and differences between the academic debate before and after the GFC. The evidence found allows academics to be guided in their high-impact research in business and management using MCDM methodologies to address contemporary challenges. An important contribution of this study is to detect gaps in the literature, highlighting unclosed gaps and emerging trends in the field of study for journal editors.

]]>Axioms doi: 10.3390/axioms11100514

Authors: Paulo Eduardo García-Nava Luis Alberto Rodríguez-Picón Luis Carlos Méndez-González Iván Juan Carlos Pérez-Olguín

Competitiveness motivates organizations to implement statistical approaches for improvement purposes. The literature offers a variety of quantitative methods intended to analyze and improve processes such as the design of experiments, steepest paths and stopping rules that search optimum responses. The objective of this paper is to run a first-order experiment to develop a steepest ascent path to subsequently apply three stopping rules (Myers and Khuri stopping rule, recursive parabolic rule and recursive parabolic rule enhanced) to identify the optimum experimentation stop from two different simulated cases. The method includes the consideration of the case study, the fitting of a linear model, the development of the steepest path and the application of stopping rules. Results suggest that procedures&rsquo; performances are similar when the response obeys a parametric function and differ when the response exhibits stochastic behavior. The discussion section shows a structured analysis to visualize these results and the output of each of the stopping rules in the two analyzed cases.

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Authors: Orietta Nicolis Luis M. Riquelme Quezada Germán Ibacache-Pulgar

In this work, the case of a Cox Process with Folded Normal Intensity (CP-FNI), in which the intensity is given by &Lambda;(t)=|Z(t)|, where Z(t) is a stationary Gaussian process, is studied. Here, two particular cases are dealt with: (i) when the process Z(t) constitutes a family of independent random variables and with a common probability law N(0,1), and (ii) the case in which Z(t) is a second order stationary process, with exponential type covariance function. In these cases, we observe that the properties of the Gaussian process Z(t) are naturally transferred to the intensity &Lambda;(t) and that very analytical results are achievable from the analytical point of view for the point process N(t). Finally, some simulations are presented in order to appreciate what type of counting phenomena can be modeled by these cases of CP-FNI. In particular, it is interesting to see how the trajectories show a tendency of the events to be grouped in certain periods of time, also leaving long periods of time without the occurrence of events.

]]>Axioms doi: 10.3390/axioms11100512

Authors: Alina Alb Alb Lupaş

In this article we explore several applications of q-calculus in geometric function theory. Using the method of differential subordination, we obtain interesting univalence properties for the q-S&#259;l&#259;gean differential operator. Sharp subordination results are obtained by using functions with remarkable geometric properties as subordinating functions and considering the conditions of expressions involving the q-S&#259;l&#259;gean differential operator and a convex combination using it.

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Authors: Milan Dordevic Rade Tešić Srdjan Todorović Miloš Jokić Dillip Kumar Das Željko Stević Sabahudin Vrtagic

One of the most common tools for achieving optimization and adequate production process management is linear programming (LP) in various forms. However, there are specific cases of the application of linear programming when production optimization implies several potential solutions instead of one. Exactly such a problem is solved in this paper, which integrates linear programming and a Multi-Criteria Decision-Making (MCDM) model. First, linear programming was applied to optimize production and several potential solutions lying on the line segment AB were obtained. A list of criteria was created and evaluated using the Improved Fuzzy Stepwise Weight Assessment Ratio Analysis (IMF SWARA). To obtain the final solution, a novel Rough compromise ranking of alternatives from distance to ideal solution (R-CRADIS) method was developed and verified through comparative analysis. The results show that the integration of linear programming and a Fuzzy-Rough MCDM model can be an exceptional solution for solving specific optimization problems.

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Authors: Iryna Chernega Andriy Zagorodnyuk

In this paper, we consider rings of multisets consisting of elements of a Banach algebra. We investigate the algebraic and topological structures of such rings and the properties of their homomorphisms. The rings of multisets arise as natural domains of supersymmetric functions. We introduce a complete metrizable topology on a given ring of multisets and extend some known results about structures of the rings to the general case. In addition, we consider supersymmetric polynomials and other supersymmetric functions related to these rings. This paper contains a number of examples and some discussions.

]]>Axioms doi: 10.3390/axioms11100509

Authors: Likai Liu Rekha Srivastava Jin-Lin Liu

By making use of a higher-order q-derivative operator, certain families of meromorphic q-starlike functions and meromorphic q-convex functions are introduced and studied. Several sufficient conditions and coefficient inequalities for functions in these subclasses are derived. The results presented in this article extend and generalize a number of previous results.

]]>Axioms doi: 10.3390/axioms11100508

Authors: Muhammad Tariq Soubhagya Kumar Sahoo Sotiris K. Ntouyas Omar Mutab Alsalami Asif Ali Shaikh Kamsing Nonlaopon

The main objective of this article is to introduce a new notion of convexity, i.e., modified exponential type convex function, and establish related fractional inequalities. To strengthen the argument of the paper, we introduce two new lemmas as auxiliary results and discuss some algebraic properties of the proposed notion. Considering a generalized fractional integral operator and differentiable mappings, whose initial absolute derivative at a given power is a modified exponential type convex, various improvements of the Hermite&ndash;Hadamard inequality are presented. Thanks to the main results, some generalizations about the earlier findings in the literature are recovered.

]]>Axioms doi: 10.3390/axioms11100507

Authors: Jingyi Xie Sirui Li

Motivated by the weighted averaging method for training neural networks, we study the time-fractional gradient descent (TFGD) method based on the time-fractional gradient flow and explore the influence of memory dependence on neural network training. The TFGD algorithm in this paper is studied via theoretical derivations and neural network training experiments. Compared with the common gradient descent (GD) algorithm, the optimization effect of the time-fractional gradient descent algorithm is significant when the value of fractional &alpha; is close to 1, under the condition of appropriate learning rate &eta;. The comparison is extended to experiments on the MNIST dataset with various learning rates. It is verified that the TFGD has potential advantages when the fractional &alpha; nears 0.95&sim;0.99. This suggests that the memory dependence can improve training performance of neural networks.

]]>Axioms doi: 10.3390/axioms11100506

Authors: Jamshed Khan Tahir Hussain Dania Santina Nabil Mlaiki

In this paper, we find all static, cylindrically symmetric spacetime metrics admitting homothetic symmetries. For this purpose, first we analyze the homothetic symmetry equations by an algorithm developed in Maple which gives all possible static, cylindrically symmetric metrics that may possess proper homothetic symmetry. After that, we have solved the homothetic symmetry equations for all these metrics to get the final form of homothetic symmetry vector fields. Comparing the obtained results with those of direct integration technique, it is observed that the Rif tree approach not only recovers the metrics already found by direct integration technique, but it also produces some new metrics.

]]>Axioms doi: 10.3390/axioms11100505

Authors: Samuel A. Hokamp

In this paper, we characterize spaces of L&infin;-functions on a compact Hausdorff space that are invariant under a transitive and continuous group action. This work is analogous to established results concerning invariant spaces of continuous and measurable functions on a compact Hausdorff space. The case for L&infin;-functions cannot be proved in the same way when endowed with the norm-topology, but a similar argument can be used when the space of L&infin;-functions is given the weak*-topology, as we show in this paper.

]]>Axioms doi: 10.3390/axioms11100504

Authors: Faiza A. Althubyani Ahmed M. T. Abd El-Bar Mohamad A. Fawzy Ahmed M. Gemeay

This study presents a new three-parameter beta distribution defined on the unit interval, which can have increasing, decreasing, left-skewed, right-skewed, approximately symmetric, bathtub, and upside-down bathtub shaped densities, and increasing, U, and bathtub shaped hazard rates. This model can define well-known distributions with various parameters and supports, such as Kumaraswamy, beta exponential, exponential, exponentiated exponential, uniform, the generalized beta of the first kind, and beta power distributions. We present a comprehensive account of the mathematical features of the new model. Maximum likelihood methods and a Bayesian method under squared error and linear exponential loss functions are presented; also, approximate confidence intervals are obtained. We present a simulation study to compare all the results. Two real-world data sets are analyzed to demonstrate the utility and adaptability of the proposed model.

]]>Axioms doi: 10.3390/axioms11100503

Authors: Yanlin Li Rajendra Prasad Abdul Haseeb Sushil Kumar Sumeet Kumar

In the present note, we characterize Clairaut semi-invariant Riemannian maps from cosymplectic manifolds to Riemannian manifolds. Moreover, we provide a nontrivial example of such a Riemannian map.

]]>Axioms doi: 10.3390/axioms11100502

Authors: Zhiming Li Changxing Ma

Bilateral correlated data frequently arise in medical clinical studies such as otolaryngology and ophthalmology. Based on an equal correlation coefficient model, this paper mainly aimed to investigate the statistical inference for the odds ratio of two proportions in bilateral correlated data, including not only three test procedures but also four confidence interval (CI) constructions. Through iterative algorithms, all unknown parameters are estimated in order to construct the likelihood ratio, score and Wald-type tests. Furthermore, the profile likelihood CI, score CI, and Wald-type CI are obtained by the bisection root-finding algorithm. We provided another Wald-type CI based on an asymptotic normality property. The performance of the proposed tests were investigated with regard to empirical type I error rate and power, and CI methods were compared in terms of mean coverage probability and mean interval width. Numerical simulations show that the score test is more robust, and has higher power than other tests. The score CI also has a shorter interval width, and its coverage probability is closer to 0.95. A real example is used to illustrate the proposed methods.

]]>Axioms doi: 10.3390/axioms11100501

Authors: Irina Perfilieva Tam Pham Petr Ferbas

The purpose of this paper is to reduce the complexity of computing the components of the integral Fm-transform, m&ge;0, whose analytic expressions include definite integrals. We propose to use nontrivial quadrature rules with nonuniformly distributed integration points instead of the widely used Newton&ndash;Cotes formulas. As the weight function that determines orthogonality, we choose the generating function of the fuzzy partition associated with the Fm-transform. Taking into account this fact and the fact of exact integration of orthogonal polynomials, we obtain exact analytic expressions for the denominators of the components of the Fm-transformation and their approximate analytic expressions, which include only elementary arithmetic operations. This allows us to effectively estimate the components of the Fm-transformation for 0&le;m&le;3. As a side result, we obtain a new method of numerical integration, which can be recommended not only for continuous functions, but also for strongly oscillating functions. The advantage of the proposed calculation method is shown by examples.

]]>Axioms doi: 10.3390/axioms11100500

Authors: Xinming Zhang Yi Li Youhua Fan

The multi-laminated controlled release system has been widely used in the modern pharmaceutical industry because of its simple structure and safety, which can control the drug release behavior by regulating its internal parameters. To achieve three desired drug release behaviors of constant rate, linear reduction, and nonlinearity, which can be controlled by the optimization of the controllable parameters in the controlled release system, such as initial concentration and diffusion coefficient, a new regularization cuckoo search algorithm based on the cuckoo search algorithm and Tikhonov regularization method is proposed. The numerical examples confirm the stability, effectiveness, and feasibility of the proposed method. The effect of the number of model layers on the optimization results is also analyzed.

]]>Axioms doi: 10.3390/axioms11100499

Authors: You-Shyang Chen Chih-Lung (Jerome) Chou Yau-Jung (Mike) Lee Su-Fen Chen Wen-Ju Hsiao

At the beginning of 2020, the COVID-19 pandemic struck the world, affecting the pace of life and the economic behavioral patterns of people around the world, with an impact exceeding that of the 2008 financial crisis, causing a global stock market crash and even the first recorded negative oil prices. Under the impact of this pandemic, due to the global large-scale quarantine and lockdown measures, game stocks belonging to the stay-at-home economy have become the focus of investors from all over the world. Therefore, under such incentives, this study aims to construct a set of effective prediction models for the price of game stocks, which could help relevant stakeholders&mdash;especially investors&mdash;to make efficient predictions so as to achieve a profitable investment niche. Moreover, because stock prices have the characteristics of a time series, and based on the relevant discussion in the literature, we know that ARIMA (the autoregressive integrated moving average) prediction models have excellent prediction performance. In conclusion, this study aims to establish an advanced hybrid model based on ARIMA as an excellent prediction technology for the price of game stocks, and to construct four groups of different investment strategies to determine which technical models of investment strategies are suitable for different game stocks. There are six important directions, experimental results, and research findings in the construction of advanced models: (1) In terms of the experiment, the data are collected from the daily closing prices of game-related stocks on the Taiwan Stock Exchange, and the sample range is from 2014 to 2020. (2) In terms of the performance verification, the return on investment is used as the evaluation standard to verify the availability of the ARIMA prediction model. (3) In terms of the research results, the accuracy of the model in predicting the prices of listed stocks can reach the 95% confidence interval predicted by the model 14 days after the closing price, and the OTC stocks fall within the 95% confidence interval for 3 days. (4) In terms of the empirical study of the rate of return, the investors can obtain a better rate of return than the benchmark strategy by trading the game stocks based on the indices set by the ARIMA model in this study. (5) In terms of the research findings, this study further compares the rate of return of trading strategies with reference to the ARIMA index and the rate of return of trading strategies with reference to the monitoring indicator, finding no significant difference between the two. (6) Different game stocks apply for different technical models of investment strategies.

]]>Axioms doi: 10.3390/axioms11100498

Authors: Noor Mohammed Noorani Abu Taha Zamani Mamdouh Alenezi Mohammad Shameem Priyanka Singh

DevOps (development and operations) is a collective and multidisciplinary organizational effort used by many software development organizations to build high-quality software on schedule and within budget. Implementing DevOps is challenging to implement in software organizations. The DevOps literature is far away from providing a guideline for effectively implementing DevOps in software organizations. This study is conducted with the aim to develop a readiness model by investigating the DevOps-related factors that could positively or negatively impact DevOps activities in the software industry. The identified factors are further categorized based on the internal and external aspects of the organization, using the SWOT (strengths, weaknesses, opportunities, threats) framework. This research work is conducted in three different phases: (1) investigating the factors, (2) categorizing the factors using the SWOT framework, and finally, (3) developing an analytic hierarchy process (AHP)-based readiness model of DevOps factors for use in software organizations. The findings would provide a readiness model based on the SWOT framework. The proposed framework could provide a roadmap for organizations in the software development industry to evaluate and improve their implementation approaches to implement a DevOps process.

]]>Axioms doi: 10.3390/axioms11100497

Authors: Wen Tan Xiaole Guo Xiangkai Sun

This paper is concerned with the radius of robust global error bounds for an uncertain piecewise linear inequality system where the uncertain data are assumed to be in polytope uncertain sets. We first present a dual characterization for robust global error bounds of this uncertain piecewise linear inequality system. Then, we establish upper and lower bounds for the radius of robust global error bounds of the system of uncertain piecewise linear inequalities in terms of the Minkowski function generalized by the polytope uncertain sets. Moreover, we also investigate robust global error bounds for this uncertain piecewise linear inequality system when the uncertain polytope sets are symmetric sets.

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Authors: Rui Ma Mengmeng Li

In this paper we investigate a forced perturbed non-instantaneous impulsive model. Firstly, we prove the existence and uniqueness of an almost periodic solution for the model considered by the Banach contraction principle. Secondly, we prove that all solutions converge exponentially to the almost periodic solution. In other words, the solution of the model considered is exponentially stable. Finally, we provide some simulations to show the effectiveness of the theoretical results.

]]>Axioms doi: 10.3390/axioms11100495

Authors: Xinxin Feng Sirui Li

The Doi&ndash;Onsager molecular theory is capable of providing a rather accurate description of the local behavior of molecules; however, its computation is extremely time-consuming, since some higher-dimensional variables are typically involved. Therefore, establishing a computable reduced model that can capture essential physical properties is an important issue. In this work, we derived a reduced Q-tensor hydrodynamic theory that described smectic phases with density variations from the Doi&ndash;Onsager molecular theory using the Bingham closure approximation. The coefficients in the tensor model were derived from those in the molecular model. The energy dissipation law was inherited from the tensor model. Some special cases for the model were also discussed.

]]>Axioms doi: 10.3390/axioms11100494

Authors: Muhammad Sabil Ur Rehman Qazi Zahoor Ahmad Isra Al-shbeil Sarfraz Ahmad Ajmal Khan Bilal Khan Jianhua Gong

In the current work, by using the familiar q-calculus, first, we study certain generalized conic-type regions. We then introduce and study a subclass of the multivalent q-starlike functions that map the open unit disk into the generalized conic domain. Next, we study potentially effective outcomes such as sufficient restrictions and the Fekete&ndash;Szeg&ouml; type inequalities. We attain lower bounds for the ratio of a good few functions related to this lately established class and sequences of the partial sums. Furthermore, we acquire a number of attributes of the corresponding class of q-starlike functions having negative Taylor&ndash;Maclaurin coefficients, including distortion theorems. Moreover, various important corollaries are carried out. The new explorations appear to be in line with a good few prior commissions and the current area of our recent investigation.

]]>Axioms doi: 10.3390/axioms11100493

Authors: Xiaohua Yang Hao Yang Jing Bao Xin Shen Rong Yan Nan Pan

As one of the most important water conservancy projects, reservoirs use water resources to achieve essential functions, such as irrigation, flood control, and power generation, by intercepting rivers. As climate extremes and global warming increase, the world&rsquo;s water reserves are being tested, and reservoir operators are being challenged. This paper investigates the optimal allocation of shared resources for hydropower to achieve rational decisions for reservoir operations. Firstly, a power resource model is constructed based on the real hydroelectric generator theory. Furthermore, based on the established power resource model combined with the influence of weather type and multi-region heterogeneous demand, this paper constructs a multi-objective hydropower shared resource allocation optimization model, with the lowest hydropower resource supply cost and the shortest time hydropower resource supply time as the optimization objectives. Secondly, for the problem that the traditional population intelligence algorithm easily falls into the local optimum when solving complex problems, the improvement of the MOPSO algorithm is completed by introducing the Levy flight strategy and differential evolution. Finally, simulation experiments were carried out, and cutting-edge algorithms, such as the GA algorithm and WOA algorithm, were selected for simulation comparison to verify the effectiveness of the constructed model and algorithm. The simulation results show that the research in this paper can contribute to effective decision-making for reservoir operators and promote intelligent reservoir operation.

]]>Axioms doi: 10.3390/axioms11100492

Authors: Rahul Shukla

The principal objective of this paper is to find the solution to a constrained minimization problem and the zero of the monotone operator in geodesic spaces. The basic tool in our study is a nonexpansive mapping. Further, we employ the general Picard&ndash;Mann iterative method to approximate fixed points of nonexpansive mappings under various conditions. We obtain certain theorems concerning &Delta; and strong convergence.

]]>Axioms doi: 10.3390/axioms11100491

Authors: Xin Du Weifeng Pan Bo Jiang Luyun Ding Yun Pan Chengxiang Yuan Yiming Xiang

Researchers have proposed many approaches to identify key classes in software from the perspective of complex networks, such as CONN-TOTAL-W, PageRankBR, and ElementRank, which can effectively help developers understand software. However, these approaches tend to rely on a single metric when measuring the importance of classes. They do not consider the aggregation of multiple metrics to select the winner classes that rank high in majority metrics. In this work, we propose a key class identification approach using Markov-Chain-based ranking aggregation, namely CRA. First, CRA constructs a weighted directed class coupling network (WDCCNet) to describe the software and further applies existing approaches on WDCCNet to calculate class importance. Second, CRA filters out some metrics according to specific rules and uses the Markov chain to aggregate the remaining metrics. When the state probability distribution reaches a fixed point and does not change anymore, the classes in the software are sorted in a descending order according to the probability distribution, and the top-15% classes are treated as key classes. To evaluate the CRA approach, we compare it with 10 baseline approaches available on 6 pieces of software. Empirical results show that our approach is superior to the baselines according to the average ranking of the Friedman Test.

]]>Axioms doi: 10.3390/axioms11100490

Authors: SidAhmed Benchiha Amer Ibrahim Al-Omari Ghadah Alomani

This paper deals with the problem of goodness-of-fit tests (GFTs) for the weighted generalized quasi-Lindley distribution (WGQLD) using ranked set sampling (RSS) and simple random sampling (SRS) techniques. The tests are based on the empirical distribution function and sample entropy. These tests include the Kullback&ndash;Leibler, Kolomogorov&ndash;Smirnov, Anderson&ndash;Darling, Cram&eacute;r&ndash;von Mises, Zhang, Liao, and Shimokawa, and Watson tests. The critical values (CV) and power of each test are obtained based on a simulation study by using SRS and RSS methods considering various sample sizes and alternatives. A rain data set is used to investigate the effectiveness of the suggested GFTs. Based on the same number of measured units for the various alternatives taken into consideration in this study, it is discovered that the RSS tests are more effective than those of their rivals in SRS. Additionally, as the set size increases, the GFTs&rsquo; power increases.

]]>Axioms doi: 10.3390/axioms11100489

Authors: Sunny Mishra Amit K. Shukla Pranab K. Muhuri

An explainable artificial intelligence (XAI) agent is an autonomous agent that uses a fundamental XAI model at its core to perceive its environment and suggests actions to be performed. One of the significant challenges for these XAI agents is performing their operation efficiently, which is governed by the underlying inference and optimization system. Along similar lines, an Explainable Fuzzy AI Challenge (XFC 2022) competition was launched, whose principal objective was to develop a fully autonomous and optimized XAI algorithm that could play the Python arcade game &ldquo;Asteroid Smasher&rdquo;. This research first investigates inference models to implement an efficient (XAI) agent using rule-based fuzzy systems. We also discuss the proposed approach (which won the competition) to attain efficiency in the XAI algorithm. We have explored the potential of the widely used Mamdani- and TSK-based fuzzy inference systems and investigated which model might have a more optimized implementation. Even though the TSK-based model outperforms Mamdani in several applications, no empirical evidence suggests this will also be applicable in implementing an XAI agent. The experimentations are then performed to find a better-performing inference system in a fast-paced environment. The thorough analysis recommends more robust and efficient TSK-based XAI agents than Mamdani-based fuzzy inference systems.

]]>Axioms doi: 10.3390/axioms11090488

Authors: Dinesh Kumar Frédéric Yves Ayant Clemente Cesarano

In the present article, we give analytical solutions for temperature distribution in a rectangular parallelepiped with the help of a multivariable I-function. The results established in this paper are of a general character from which several known and new results can be deduced. We also give the special and particular cases of our main findings.

]]>Axioms doi: 10.3390/axioms11090487

Authors: Muhammad Shafii Abubakar Kazeem Olalekan Aremu Maggie Aphane

In this article, we introduce the neighborhood versions of two classical topological indices, namely neighborhood geometric&ndash;arithmetic and neighborhood atom bond connectivity indices. We study the graph-theoretic properties of these new topological indices for some known graphs, e.g., complete graph Kn, regular graph Rn, cycle graph Cn, star graph Sn, pendant graph, and irregular graph and further establish their respective bounds. We note that the neighbourhood geometric&ndash;arithmetic index of Kn, Rn, Cn, and Sn is equal to the number of edges. The neighborhood atom bond connectivity index of an arbitrary simple graph G is strictly less than the number of edges. Our results contribute to the literature in this direction.

]]>Axioms doi: 10.3390/axioms11090486

Authors: Haim Cohen Yinon Nachshon Anat Maril Paz M. Naim Jürgen Jost Emil Saucan

Temporal information plays a central role in shaping the structure of a network. In this paper, we consider the impact of an object on network structure over time. More specifically, we use a novel object-based dynamic measure to reflect the extent to which an object that is represented in the network by a vertex affects the topology of the network over time. By way of multigraph and Forman&ndash;Ricci flow, we assess the object&rsquo;s impact on graph weights by comparing two graphs, one in which the object is present and one in which the object is absent. After using a case study to demonstrate the impact of Forman&ndash;Ricci flow on the network structure, we apply our measure in a semantic network to assess the effects of a word on the interactions between other words that follow it. In addition, we compare our novel measure to centrality and curvature measures so that we can ascertain the advantages of our measure over ones that already exist.

]]>Axioms doi: 10.3390/axioms11090485

Authors: Ivette Miramontes Patricia Melin

Optimization is essential for applications since it can improve the results provided in different areas; for this task, it is beneficial to use soft computing techniques, such as bio-inspired algorithms. In addition, it has been shown that if dynamic parameter adaptation is applied to these algorithms, they can provide a better result. For this work, the main contribution is to carry out the dynamic parameter adaptation to the bird swarm algorithm using interval type-2 fuzzy systems to realize a new fuzzy bio-inspired algorithm. The design of the proposed fuzzy system consists of two inputs corresponding to the iterations and diversity. As outputs, it takes the values of C and S, which are parameters to be adjusted by the algorithm. Once the design and the experimentation are realized, they are divided into two study cases. The first consists of a set of complex functions of the Congress of Evolutionary Competition 2017. The second case study consists of optimizing the membership functions in a fuzzy system designed to provide the nocturnal blood pressure profile, which corresponds to a neuro-fuzzy hybrid model to obtain the risk of hypertension. Analyzing the 30 experiments performed in both case studies, we can observe that the results obtained are improved when compared with the original method and other proposed methodologies, achieving good results in the complex functions. In addition, the optimized fuzzy system will reach an average of 97% correct classification. Statistically, it can be concluded that there is significant evidence to affirm that the proposed method provides good results.

]]>Axioms doi: 10.3390/axioms11090484

Authors: Rui Chen Jianping Li Weihua He

Graph robustness or network robustness is the ability that a graph or a network preserves its connectivity or other properties after the loss of vertices and edges, which has been a central problem in the research of complex networks. In this paper, we introduce the Modified Zagreb index and Modified Zagreb index centrality as novel measures to study graph robustness. We theoretically find some relationships between these novel measures and some other graph measures. Then, we use Modified Zagreb index centrality to analyze the robustness of BA scale-free networks, ER random graphs and WS small world networks under deliberate or random vertex attacks. We also study the correlations between this new measure and some other existed measures. Finally, we use Modified Zagreb index centrality to study the robustness of two real world networks. All these results demonstrate the efficiency of Modified Zagreb index centrality for assessing the graph robustness.

]]>Axioms doi: 10.3390/axioms11090483

Authors: Khalid Abdulaziz Alnowibet Ahmad M. Alshamrani Adel Fahad Alrasheedi Salem Mahdi Mahmoud El-Alem Abdallah Aboutahoun Ali Wagdy Mohamed

In this paper, a new Modified Meta-Heuristic algorithm is proposed. This method contains some modifications to improve the performance of the simulated-annealing algorithm (SA). Most authors who deal with improving the SA algorithm presented some improvements and modifications to one or more of the five standard features of the SA algorithm. In this paper, we improve the SA algorithm by presenting some suggestions and modifications to all five standard features of the SA algorithm. Through these suggestions and modifications, we obtained a new algorithm that finds the approximate solution to the global minimum of a non-convex function. The new algorithm contains novel parameters, which are updated at each iteration. Therefore, the variety and alternatives in choosing these parameters demonstrated a noticeable impact on the performance of the proposed algorithm. Furthermore, it has multiple formulas by which the candidate solutions are generated. Diversity in these formulas helped the proposed algorithm to escape a local point while finding the global minimizer of a non-convex function. The efficiency of the proposed algorithm is reported through extensive numerical experiments on some well-known test problems. The performance profiles are used to evaluate and compare the performance of our proposed algorithm against the other five meta-heuristic algorithms. The comparison results between the performance of our suggested algorithm and the other five algorithms indicate that the proposed algorithm is competitive with, and in all cases superior to, the five algorithms in terms of the efficiency, reliability, and effectiveness for finding the global minimizers of non-convex functions. This superiority of the new proposed algorithm is due to those five modified standard features.

]]>Axioms doi: 10.3390/axioms11090482

Authors: Henok Desalegn Desta Deepak B. Pachpatte Jebessa B. Mijena Tadesse Abdi

In this paper, we obtain some univariate and multivariate Ostrowski-type inequalities using the Atangana&ndash;Baleanu fractional derivative in the sense of Liouville&ndash;Caputo (ABC). The results obtained for both left and right ABC fractional derivatives can be applied to study further fractional inequalities and estimate various non-local function problems since the operator consists of a non-singular kernel. The obtained results are more generalized in nature.

]]>Axioms doi: 10.3390/axioms11090481

Authors: Zhili Huang Jinli Li Hongge Yue

With the development of science and technology, people&rsquo;s travel modes have become more diversified, and self-balancing vehicles have become a popular travel tool for young people. However, in recent years, due to its quality instability, many regions have issued relevant bans, affecting the development of the balanced vehicle industry. In order to better understand balancing vehicle technology, this paper starts with the balancing vehicle patent, and carries out the following research: This paper first introduces the background and current situation of balanced vehicles and the patent. Then, the principle and model of multi-attribute decision-making based on the analytic hierarchy process (AHP-MADM) are described. According to the three-dimensional patent valuation system issued by the State Intellectual Property Office, a core patent valuation system is established. Then, the weights of patent evaluation attributes are calculated by the improved AHP. After, the patent value of the self-balancing vehicle is evaluated using the established AHP-MADM model. On this basis, the status of patent research and the development of self-balancing vehicles is studied to provide a reference for relevant industry personnel, especially R &amp; D personnel, in future product technology updates and patent layout.

]]>Axioms doi: 10.3390/axioms11090479

Authors: Seong-Hoon Cho

In this paper, the concepts of Suzuki-type &#8466;&gamma; contractions and Suzuki&ndash;Berinde-type &#8466;&gamma; contractions are introduced, and new fixed-point theorems for these two contractions are established.

]]>Axioms doi: 10.3390/axioms11090480

Authors: Yingying Wang Jin Tao Haitao Gao

To extract more accurate and abundant features of corn disease and solve the problems of rough classification and low recognition accuracy, the attention mechanism is introduced into the field of corn disease recognition. The corn disease recognition model (AT-AlexNet) is proposed based on an attention mechanism. The network was based on AlexNet, and the new down-sampling attention module was constructed to enhance the foreground response of the disease; the Mish activation function was introduced to improve the nonlinear expression of the network; the new module of the full connection layer was designed to reduce the network parameters. In the experiment of the enhanced corn disease datasets, the average recognition accuracy of the attention-based network model AT-AlexNet is 99.35%. The recognition accuracy of using the Mish activation function is 0.65% higher than that of the ReLu activation function. The experiments show that compared with other identification methods, the proposed method has better classification performance for corn diseases.

]]>Axioms doi: 10.3390/axioms11090478

Authors: Myroslav Sheremeta

For analytic functions fj(z)=&sum;n=0&infin;an,jzn, 1&le;j&le;p, the notion of a Hadamard composition (f1&lowast;&hellip;&lowast;fp)m=&sum;n=0&infin;&sum;k1+&#8943;+kp=mck1&hellip;kpan,1k1&middot;&hellip;&middot;an,pkpzn of genus m is introduced. The relationship between the growth of the Gelfond&ndash;Leont&rsquo;ev derivative of the Hadamard composition of functions fj and the growth Hadamard composition of Gelfond&ndash;Leont&rsquo;ev derivatives of these functions is studied. We found conditions under which these derivatives and the composition have the same order and a lower order. For the maximal terms of the power expansion of these derivatives, I describe behavior of their ratios.

]]>Axioms doi: 10.3390/axioms11090477

Authors: Siqintuya Jin Muhammet Cihat Dağli Feng Qi

In this paper, by introducing degenerate Fubini-type polynomials, with the help of the Fa&agrave; di Bruno formula and some properties of partial Bell polynomials, the authors provide several new explicit formulas and recurrence relations for Fubini-type polynomials and numbers, associate the newly defined degenerate Fubini-type polynomials with degenerate Apostol&ndash;Bernoulli polynomials and degenerate Apostol&ndash;Euler polynomials of order &alpha;. These results enable one to present additional relations for some degenerate special polynomials and numbers.

]]>Axioms doi: 10.3390/axioms11090476

Authors: Zi-Qiang Wang Ming-Dan Long Jun-Ying Cao

In this paper, we present a high-order approximate solution with uniform accuracy for nonlinear 3D Volterra integral equations. This numerical scheme is constructed based on the three-dimensional block cubic Lagrangian interpolation method. At the same time, we give the local truncation error analysis of the numerical scheme based on Taylor&rsquo;s theorem. Through theoretical analysis, we reach the conclusion that the optimal convergence order of this high-order numerical scheme is 4. Finally, we verify the effectiveness and applicability of the method through four numerical examples.

]]>Axioms doi: 10.3390/axioms11090475

Authors: Xinyue Zhu Wei Li Xueping Luo

In this paper, we introduce and study a new class of differential set-valued inverse variational inequalities in finite dimensional spaces. By applying a result on differential inclusions involving an upper semicontinuous set-valued mapping with closed convex values, we first prove the existence of Carath&eacute;odory weak solutions for differential set-valued inverse variational inequalities. Then, by the existence result, we establish the stability for the differential set-valued inverse variational inequality problem when the constraint set and the mapping are perturbed by two different parameters. The closedness and continuity of Carath&eacute;odory weak solutions with respect to the two different parameters are obtained.

]]>Axioms doi: 10.3390/axioms11090474

Authors: Kuei-Hu Chang

When major emergencies or accidents occur, risk evaluation and prediction are the most important means to reduce their impact. Typical risk evaluation uses the failure mode and effects analysis (FMEA) method for failure-risk ranking and control. However, when faced with severe special infectious diseases such as COVID-19, there are many cognitive and information uncertainties that the FMEA method is unable to effectively handle. To effectively deal with the issue of risk evaluation when major emergencies or accidents occur, this paper integrated the risk-priority number and spherical fuzzy-sets methods to propose a novel emergency-risk-evaluation method. In the numerical verification, this paper applied the example of preventing secondary COVID-19 transmissions in hospitals to explain the calculation procedure and validity of the proposed new emergency-risk-evaluation approach. The calculation results were also compared with the typical RPN, fuzzy-set, and intuitionistic fuzzy-set methods. The calculation results showed that the proposed new emergency-risk-evaluation approach could effectively handle the cognitive and informational uncertainties of emergency-risk-evaluation issues during the COVID-19 pandemic.

]]>Axioms doi: 10.3390/axioms11090473

Authors: Hovik A. Matevossian Maria V. Korovina Vladimir A. Vestyak

The paper is devoted to studying the behavior of solutions of the Cauchy problem for large values of time&mdash;more precisely, obtaining an asymptotic expansion characterizing the behavior of the solution of the Cauchy problem for a one-dimensional second-order hyperbolic equation with periodic coefficients for large values of the time parameter t. To obtain this asymptotic expansion as t&rarr;&infin;, methods of the spectral theory of differential operators are used, as well as the properties of the spectrum of a non-positive Hill operator with periodic coefficients.

]]>Axioms doi: 10.3390/axioms11090472

Authors: Yong Zhang Huan-He Dong Yong Fang

The KP hierarchy reduction method is one of the most reliable and efficient techniques for determining exact solitary wave solutions to nonlinear partial differential equations. In this paper, according to the KP hierarchy reduction technique, rational and some other semi-rational solutions to the (2 + 1)-dimensional Maccari system are investigated. It is shown that two different types of breathers can be derived, and under appropriate parameter constraints, they can be reduced to some well known solutions, involving the homoclinic orbits, dark soliton or anti-dark soliton solution. For the dark and anti-dark solution, its interaction is similar to a resonance soliton. Furthermore, by using a limiting technique, we derive two kinds of rational solutions, one is the lump and the other one is the rogue wave. After constructing these solutions, we further discuss the interactions between the obtained solutions. It is interesting that we obtain a parallel breather and a intersectional breather, which seems very surprising. Finally, we also provide a new three-state interaction, which is composed by the dark-soliton, rogue wave and breather and has never been provided for the Maccari system.

]]>Axioms doi: 10.3390/axioms11090471

Authors: Rui Liu Michal Fečkan Donal O’Regan Jinrong Wang

In this paper, we investigate the controllability of first-order impulsive fuzzy differential equations. Using the direct construction method, the controllability of first-order linear impulsive fuzzy differential equations is considered with a&lt;0, the (c1) solution, and a&lt;0, the (c2) solution, respectively.In addition, by employing the Banach fixed-point theorem, the controllability of first-order nonlinear impulsive fuzzy differential equations is studied. Finally, examples are presented to illustrate our theoretical results.

]]>Axioms doi: 10.3390/axioms11090470

Authors: Austine Efut Ofem Aftab Hussain Oboyi Joseph Mfon Okon Udo Umar Ishtiaq Hamed Al Sulami Chukwuka Fernando Chikwe

In this article, we develop a faster iteration method, called the A&lowast;&lowast; iteration method, for approximating the fixed points of almost contraction mappings and generalized &alpha;-nonexpansive mappings. We establish some weak and strong convergence results of the A&lowast;&lowast; iteration method for fixed points of generalized &alpha;-nonexpansive mappings in uniformly convex Banach spaces. We provide a numerical example to illustrate the efficiency of our new iteration method. The weak w2-stability result of the new iteration method is also studied. As an application of our main results, we approximate the solution of a fractional Volterra&ndash;Fredholm integro-differential equation. Our results improve and generalize several well-known results in the current literature.

]]>Axioms doi: 10.3390/axioms11090469

Authors: Alhasan Alkuhlani Walaa Gad Mohamed Roushdy Michael Gr. Voskoglou Abdel-badeeh M. Salem

Post-translational glycosylation and glycation are common types of protein post-translational modifications (PTMs) in which glycan binds to protein enzymatically or nonenzymatically, respectively. They are associated with various diseases such as coronavirus, Alzheimer&rsquo;s, cancer, and diabetes diseases. Identifying glycosylation and glycation sites is significant to understanding their biological mechanisms. However, utilizing experimental laboratory tools to identify PTM sites is time-consuming and costly. In contrast, computational methods based on machine learning are becoming increasingly essential for PTM site prediction due to their higher performance and lower cost. In recent years, advances in Transformer-based Language Models based on deep learning have been transferred from Natural Language Processing (NLP) into the proteomics field by developing language models for protein sequence representation known as Protein Language Models (PLMs). In this work, we proposed a novel method, PTG-PLM, for improving the performance of PTM glycosylation and glycation site prediction. PTG-PLM is based on convolutional neural networks (CNNs) and embedding extracted from six recent PLMs including ProtBert-BFD, ProtBert, ProtAlbert, ProtXlnet, ESM-1b, and TAPE. The model is trained and evaluated on two public datasets for glycosylation and glycation site prediction. The results show that PTG-PLM based on ESM-1b and ProtBert-BFD has better performance than PTG-PLM based on the other PLMs. Comparison results with the existing tools and representative supervised learning methods show that PTG-PLM surpasses the other models for glycosylation and glycation site prediction. The outstanding performance results of PTG-PLM indicate that it can be used to predict the sites of the other types of PTMs.

]]>Axioms doi: 10.3390/axioms11090468

Authors: Sumit Som Moosa Gabeleh Manuel De la Sen

In the year 2014, Almeida et al. introduced a new class of mappings, namely, contractions of Geraghty type. Additionally, in the year 2021, Beg et al. introduced the concept of generalized F-proximal contraction of the first kind and generalized F-proximal contraction of the second kind, respectively. After developing these concepts, authors mainly studied the best proximity points for these classes of mappings. In this short note, we prove that the problem of the existence of the best proximity points for the said classes of proximal contractions is equivalent to the corresponding fixed points problems.

]]>Axioms doi: 10.3390/axioms11090467

Authors: Yaguai Yu Yina Yan Panyi Shen Yuting Li Taohan Ni

This paper combines the green industrial strategy and green financial policies for the construction industry implemented in China in the context of carbon neutrality. A total of 67 listed companies in the construction industry from 2017 to 2020 were taken as the research sample, the green financing efficiency was measured, and its influencing factors were identified based on the three-stage DEA and systematic GMM method. The findings show that the green financing efficiency of listed companies in the construction industry is not high overall, although it is increasing. There are obvious differences in subsectors, among which, the efficiency of architectural design and service industries is relatively high. Overall, the financial environment, and the interaction between the government and the financial market, significantly and positively influence the green financing efficiency. In addition, the macroeconomic environment and the government&ndash;enterprise relationship has a complex impact on the green financing efficiency. The ownership concentration and having corporate executives with a financial background have a significant positive impact on the green financing efficiency, and the enterprise size, the debt maturity structure, and the R&amp;D and innovation capability have a significant negative impact. The findings of this paper have implications for the improvement of the policy system that supports green development in the construction industry, and provide guidance for the strategic adjustment of the construction industry itself.

]]>Axioms doi: 10.3390/axioms11090466

Authors: Junke Kou Qinmei Huang Huijun Guo

This paper considers an unknown functional estimation problem in a regression model with multiplicative and additive noise. A linear wavelet estimator is first constructed by a wavelet projection operator. The convergence rate under the pointwise error of linear wavelet estimators is studied in local H&ouml;lder space. A nonlinear wavelet estimator is provided by the hard thresholding method in order to obtain an adaptive estimator. The convergence rate of the nonlinear estimator is the same as the linear estimator up to a logarithmic term. Finally, it should be pointed out that the convergence rates of two wavelet estimators are consistent with the optimal convergence rate on pointwise nonparametric estimation.

]]>Axioms doi: 10.3390/axioms11090465

Authors: Fachao Li Ruya Fan Chenxia Jin

This study considers the team recommendation problem as a generalized assignment problem. Firstly, a formal description of the team recommendation problem is given; secondly, a team-recommended generalized assignment model (TRGAM) is established based on the work ability value of alternative members, the comprehensive work ability value of the team as the core concern index, the importance weight of team tasks and the energy allocation weight of team members as the fusion strategy of the data; thirdly, a solution method for the standard case of TRGAM is designed using the enumeration method and Hungarian algorithms (BEM&oplus;HM&ndash;TRGAMs) as local computational tools; fourthly, the alternative member set refinement methods and standardization measures for TRGAM are given; finally, BEM&oplus;HM&ndash;TRGAMs are analyzed using specific arithmetic examples. The theoretical analysis and experimental results show that TRGAM has good structural features and interpretability and BEM&oplus;HM&ndash;TRGAMs can effectively solve the TRGAM solving problem.

]]>Axioms doi: 10.3390/axioms11090464

Authors: Alejandro Chinea Manrique de Lara Elka Korutcheva

The evolution analysis of networks whose links are either positive or negative, representing opposite relationships such as friendship and enmity, has been revealed to be particularly useful in sociological contexts. Using a large relational dataset containing the last two centuries of state-wise geopolitical information (the correlates of war&ndash;alliance conflicts), a machine learning approach is presented to predict network dynamics. The combination of geometric as well as information&ndash;theoretic measures to characterize the resulting discrete time series together with the power of deep learning machines is used to generate a model whose predictions are even accurate on the few days in two centuries of international relations when the typical value (i.e., Alliance or Neutral) changed to a war or a conflict. In other words, the model can predict the next state of the network with a probability of error close to zero.

]]>Axioms doi: 10.3390/axioms11090463

Authors: Pavel Praks Marek Lampart Renáta Praksová Dejan Brkić Tomáš Kozubek Jan Najser

In this paper, we analyze the interpretable models from real gasification datasets of the project &ldquo;Centre for Energy and Environmental Technologies&rdquo; (CEET) discovered by symbolic regression. To evaluate CEET models based on input data, two different statistical metrics to quantify their accuracy are usually used: Mean Square Error (MSE) and the Pearson Correlation Coefficient (PCC). However, if the testing points and the points used to construct the models are not chosen randomly from the continuum of the input variable, but instead from the limited number of discrete input points, the behavior of the model between such points very possibly will not fit well the physical essence of the modelled phenomenon. For example, the developed model can have unexpected oscillatory tendencies between the used points, while the usually used statistical metrics cannot detect these anomalies. However, using dynamic system criteria in addition to statistical metrics, such suspicious models that do fit well-expected behavior can be automatically detected and abandoned. This communication will show the universal method based on dynamic system criteria which can detect suitable models among all those which have good properties following statistical metrics. The dynamic system criteria measure the complexity of the candidate models using approximate and sample entropy. The examples are given for waste gasification where the output data (percentage of each particular gas in the produced mixture) is given only for six values of the input data (temperature in the chamber in which the process takes place). In such cases instead, to produce expected simple spline-like curves, artificial intelligence tools can produce inappropriate oscillatory curves with sharp picks due to the known tendency of symbolic regression to produce overfitted and relatively more complex models if the nature of the physical model is simple.

]]>Axioms doi: 10.3390/axioms11090462

Authors: Se Yoon Lee

It is typically difficult to estimate the number of degrees of freedom due to the leptokurtic nature of the Student t-distribution. Particularly in studies with small sample sizes, special care is needed concerning prior choice in order to ensure that the analysis is not overly dominated by any prior distribution. In this article, popular priors used in the existing literature are examined by characterizing their distributional properties on an effective support where it is desirable to concentrate on most of the prior probability mass. Additionally, we suggest a log-normal prior as a viable prior option. We show that the Bayesian estimator based on a log-normal prior compares favorably to other Bayesian estimators based on the priors previously proposed via simulation studies and financial applications.

]]>Axioms doi: 10.3390/axioms11090461

Authors: Abdul Haseeb Mohd Bilal Sudhakar K. Chaubey Mohammad Nazrul Islam Khan

In this paper, we study the properties of &#1013;-Kenmotsu manifolds if its metrics are *&eta;-Ricci-Yamabe solitons. It is proven that an &#1013;-Kenmotsu manifold endowed with a *&eta;-Ricci-Yamabe soliton is &eta;-Einstein. The necessary conditions for an &#1013;-Kenmotsu manifold, whose metric is a *&eta;-Ricci-Yamabe soliton, to be an Einstein manifold are derived. Finally, we model an indefinite Kenmotsu manifold example of dimension 5 to examine the existence *&eta;-Ricci-Yamabe solitons.

]]>Axioms doi: 10.3390/axioms11090460

Authors: Taras Vasylyshyn Kostiantyn Zhyhallo

The class of measure spaces which can be represented as unions of Lebesgue-Rohlin spaces with continuous measures contains a lot of important examples, such as Rn for any n&isin;N with the Lebesgue measure. In this work we consider symmetric functions on Banach spaces of all complex-valued integrable essentially bounded functions on such unions. We construct countable algebraic bases of algebras of continuous symmetric polynomials on these Banach spaces. The completions of such algebras of polynomials are Fr&eacute;chet algebras of all complex-valued entire symmetric functions of bounded type on the abovementioned Banach spaces. We show that each such Fr&eacute;chet algebra is isomorphic to the Fr&eacute;chet algebra of all complex-valued entire symmetric functions of bounded type on the complex Banach space of all complex-valued essentially bounded functions on [0,1].

]]>Axioms doi: 10.3390/axioms11090459

Authors: Refah Alotaibi Mazen Nassar Indranil Ghosh Hoda Rezk Ahmed Elshahhat

The univariate alpha power exponential (APE) distribution has several appealing characteristics. It behaves similarly to Weibull, Gamma, and generalized exponential distributions with two parameters. In this paper, we consider different bivariate mixture models starting with two independent univariate APE models, and, in the latter case, starting from two dependent APE models. Several useful structural properties of such a mixture model (under the assumption of two independent APE distribution) are discussed. Bivariate APE (BAPE), in short, modelled under the dependent set up are also discussed in the context of a copula-based construction. Inferential aspects under the classical and under the Bayesian paradigm are considered to estimate the model parameters, and a simulation study is conducted for this purpose. For illustrative purposes, a well-known motor data is re-analyzed to exhibit the flexibility of the proposed bivariate mixture model.

]]>Axioms doi: 10.3390/axioms11090458

Authors: Huaping Huang Wei-Shih Du

In this paper, we present some generalizations and improvements of a new integral inequality from the 29th IMC in 2022. Some applications of our new results are also provided.

]]>Axioms doi: 10.3390/axioms11090457

Authors: Diego Ortega Elka Korutcheva

Segregation affects millions of urban dwellers. The main expression of this reality is the creation of ghettos which are city parts characterized by a combination of features: low income, poor cultural level&hellip; Segregation models have been usually defined over regular lattices. However, in recent years, the focus has shifted from these unrealistic frameworks to other environments defined via geographic information systems (GIS) or networks. Nevertheless, each one of them has its drawbacks: GIS demands high-resolution data, that are not always available, and networks tend to have limited real-world applications. Our work tries to fill the gap between them. First, we use some basic GIS information to define the network, and then, run an extended Schelling model on it. As a result, we obtain the location of ghettos. After that, we analyze which parts of the city are segregated, via spatial analysis and machine learning and compare our results. For the case study of Washington D.C., we obtain an 80% accuracy.

]]>Axioms doi: 10.3390/axioms11090456

Authors: Kavita Jain Akash Saxena Ahmad M. Alshamrani Adel Fahad Alrasheedi Khalid Abdulaziz Alnowibet Ali Wagdy Mohamed

Successful privatization in other sectors leads to a restructuring in the power sector. The same practice has been adopted in the electrical industry with a deregulated electricity market (EM). This enables competition among generating companies (Genco&rsquo;s) for maximizing their profit and it plays a central role. With this aim, each Genco gives a higher bid that may result in a risk of losing the opportunity to get selected at auction. The big challenge in front of a Genco is to acquire an optimal bid and this process is known as the Optimal Bidding Strategy (OBS) of a Genco. In this manuscript, a new variant of whale optimization (WOA) termed the Amended Whale Optimization Algorithm (AWOA) is proposed, to attain the OBS of thermal Genco in an EM. Once the effectiveness of new AWOA is proved on 23 benchmark functions, it is applied to five Genco strategic bidding problems in a spot market with uniform price. The results obtained from the proposed AWOA are compared with other competitive algorithms. The results reflect that AWOA outperforms in terms of the profit and convergence rate. Simulations also indicate that the proposed AWOA can successfully be used for an OBS in the EM.

]]>Axioms doi: 10.3390/axioms11090455

Authors: Manal M. Yousef Amal S. Hassan Huda M. Alshanbari Abdal-Aziz H. El-Bagoury Ehab M. Almetwally

In many real-life scenarios, systems frequently perform badly in difficult operating situations. The multiple failures that take place when systems reach their lower, higher, or extreme functioning states typically receive little attention from researchers. This study uses generalized progressive hybrid censoring to discuss the inference of R=P(X&lt;Y&lt;Z) for a component when it is exposed to two stresses, Y,Z, and it has one strength X that is regarded. We assume that both the stresses and strength variables follow an exponentiated exponential distribution with a common scale parameter. We obtain R&rsquo;s maximum likelihood estimator and approximate confidence intervals. In addition, the Bayesian estimators for symmetric, such as squared error, and asymmetric loss functions, such as linear exponential, are developed. Credible intervals with the highest posterior densities are established. Monte Carlo simulations are used to evaluate and compare the effectiveness of the many proposed estimators. The process is then precisely described using an analysis of real data.

]]>Axioms doi: 10.3390/axioms11090454

Authors: Nabil Mlaiki Nihal Taş Elif Kaplan Suhad Subhi Aiadi Asma Karoui Souayah

Recently, the fixed-circle problems have been studied with different approaches as an interesting and geometric generalization. In this paper, we present some solutions to an open problem CC: what is (are) the condition(s) to make any circle C&piv;0,&sigma; as the common fixed circle for two (or more than two) self-mappings? To do this, we modify some known contractions which are used in fixed-point theorems such as the Hardy&ndash;Rogers-type contraction, Kannan-type contraction, etc.

]]>Axioms doi: 10.3390/axioms11090452

Authors: Chia-Chi Sun

With COVID-19 still making headlines around the world, many people currently feel uncertain about many aspects of life, including family financial planning and wealth management. Financial planning is important at all times, but it becomes essential during a crisis such as the coronavirus pandemic, which has disrupted people&rsquo;s finances. Some economic consequences are already apparent, but the financially-induced stress caused by the uncertainty is less visible. With the increase in family wealth and size of organizations, there is a comparable increase in their assets. There is considerable demand for professionals to manage these assets and coordinate investment activities in order to maintain growth. This raises the issue of how to increase a wealth management bank&rsquo;s competitive advantages. This study approached the issue by using experts and the application of fuzzy logic and decision-making trial and evaluation laboratory and multiple criteria decision-making to segment a set of the selection criteria used by prospective customers, to select a wealth management bank that can effectively manage personal wealth. The results showed that the management&rsquo;s learning and growth perspective was the most important factor in respondents&rsquo; selection of a wealth management bank. This paper also provides managerial practice implications.

]]>Axioms doi: 10.3390/axioms11090453

Authors: Yajing Gu Yuanguo Zhu

In this paper, we study a new type of optimal control problem subject to a parabolic uncertain partial differential equation where the expected value criterion is adopted in the objective function. The basic idea of Haar wavelet transformation is to transform the proposed problem into an approximate uncertain optimal control problem with arbitrary accuracy because the dimension of Haar basis tends to infinity. The relative convergence theorem is proved. An application to an optimal control problem with an uncertain heat equation is dealt with to illustrate the efficiency of the proposed method.

]]>Axioms doi: 10.3390/axioms11090449

Authors: Muneerah Al Nuwairan Zulqurnain Sabir

The purpose of this study is to provide a mathematical construction based on the novel singular perturbed model of the second kind (NSPM-SK) using the standard form of the Lane&ndash;Emden. The singular Lane&ndash;Emden types of the models have abundant applications in astrophysics. The inclusive features of this model are provided using the perturbed, pantograph, singular point together and the shape factor based on the NSPM-SK. These models become more complicated by using these factors through the artificial neural networks (ANNs) together with the optimization procedures of the swarming particle swarm optimization (PSO) paradigms and the local sequential quadratic programming (SQP). An objective function is provided based on the differential form of the NSPM-SK and then optimization is performed through the hybridization of the PSOSQP. The exactness of the model is attained to solve three different variations of the mathematical NSPM-SK by using the overlapping of the obtained and true results. The stability, robustness, and convergence of the designed numerical approach are perceived by using different statistical performances of the ANNs together with the optimization of the PSOSQP for 30 independent executions.

]]>Axioms doi: 10.3390/axioms11090451

Authors: Isra Al-Shbeil Abbas Kareem Wanas Afis Saliu Adriana Cătaş

In the present paper, due to beta negative binomial distribution series and Laguerre polynomials, we investigate a new family F&Sigma;(&delta;,&eta;,&lambda;,&theta;;h) of normalized holomorphic and bi-univalent functions associated with Ozaki close-to-convex functions. We provide estimates on the initial Taylor&ndash;Maclaurin coefficients and discuss Fekete&ndash;Szeg&#337; type inequality for functions in this family.

]]>Axioms doi: 10.3390/axioms11090450

Authors: Xiao Zhang Jingyi Wang Liusan Wu Ming Cheng Dongqing Zhang

The total output value of the construction industry (TOVCI) reflects its own development level to a certain extent. An accurate prediction of the construction industry&rsquo;s total output value is beneficial to the government&rsquo;s dynamic regulation. The grey prediction model is widely used for its simple calculation process and high prediction accuracy. Based on the TOVCI of China from 2017 to 2020, this paper constructs an FGM (1,1) model, calculates r by a simulated annealing algorithm, and forecasts the TOVCI of China in next few years. At present, the Particle Swarm Optimization algorithm (PSO) is employed in the calculation of r in the literature. However, the advantage of the simulated annealing algorithm is its powerful global search performance. The prediction results indicate that the TOVCI of China will continue to grow, but the growth rate will slow down. Therefore, the construction industry of China should not simply pursue the high-speed growth of the total output value, but pay more attention to high-quality development, such as technological innovation, energy conservation and environmental protection. Finally, the limitations and future research directions are elucidated.

]]>Axioms doi: 10.3390/axioms11090448

Authors: Sang-Ha Sung Jong-Min Kim Byung-Kwon Park Sangjin Kim

Cryptocurrencies are highly volatile investment assets and are difficult to predict. In this study, various cryptocurrency data are used as features to predict the log-return price of major cryptocurrencies. The original contribution of this study is the selection of the most influential major features for each cryptocurrency using the volatility features of cryptocurrency, derived from the autoregressive conditional heteroskedasticity (ARCH) and generalized autoregressive conditional heteroskedasticity (GARCH) models, along with the closing price of the cryptocurrency. In addition, we sought to predict the log-return price of cryptocurrencies by implementing various types of time-series model. Based on the selected major features, the log-return price of cryptocurrency was predicted through the autoregressive integrated moving average (ARIMA) time-series prediction model and the artificial neural network-based time-series prediction model. As a result of log-return price prediction, the neural-network-based time-series prediction models showed superior predictive power compared to the traditional time-series prediction model.

]]>Axioms doi: 10.3390/axioms11090447

Authors: Thi Bich Ha Nghiem Ta-Chung Chu

Selecting a suitable design for a lean facility layout has become a critical issue for a manufacturing company aiming to remove waste or non-value-added activities and implement the optimal facility arrangement. Many quantitative and qualitative criteria with different weights need to be considered in evaluating lean facility layout designs. To address the issue, a Best-Worst method (BWM) based on fuzzy ELECTRE I is introduced to determine the optimal lean facility layout design, in which the BWM is utilized for generating the criteria weights, and an extension of fuzzy ELECTRE I is introduced to identify the most suitable alternative. The signed distance method is employed to defuzzify the fuzzy numbers and obtain discordance matrix values. Based on the subtraction of discordance values from concordance values, a modified fuzzy ELECTRE I is introduced to evaluate alternative lean facility layout designs that can avoid missing information. A numerical example of the evaluation of lean facility layout designs for a manufacturing company is provided to show the potential of the suggested models. Comparative studies are investigated to illustrate the superiority of the suggested method.

]]>Axioms doi: 10.3390/axioms11090446

Authors: M. Nandhini R. Lavanya Juan J. Nieto

This paper develops a fractional-order model of COVID-19 with vaccination. The model is well designed by including both the efficacy and inefficacy of vaccinations in humans. Besides calculating the reproduction number, equilibrium points and the feasibility region are also determined. Stability analysis for the proposed model around equilibrium points is discussed. Fixed-point theory is employed to identify the singularity of the solution. Adomian decomposition and Laplace integral transformation are combined to obtain the solution. We present the solutions graphically to analyze the contributions of the disease dynamics based on different values of the fractional order. This study seeks an in-depth understanding of COVID-19 transmission to improve health outcomes.

]]>Axioms doi: 10.3390/axioms11090445

Authors: Kang-Jia Wang

This study focuses on investigating the modified Benjamin-Bona-Mahony equation that is used to model the long wave in nonlinear dispersive media of the optical illusion field. Two effective techniques, the variational direct method and He&rsquo;s frequency formulation method, are employed to seek the travelling wave solutions. Using these two techniques, abundant exact solutions such as the bright wave, bright-dark wave, bright-like wave, kinky-bright wave and periodic wave solutions, are obtained. The 3-D contours and 2-D curves are drawn to present the dynamic physical behaviors of the solutions by assigning the proper parameters. It shows that the proposed methods are effective but simple and only need one or two steps to construct the exact solutions, which are expected to provide some new insights to study the travelling wave solutions of the PDEs arising in physics.

]]>Axioms doi: 10.3390/axioms11090444

Authors: Yanlin Fu Qing Wu Ke Liu Haotian Gao

Extreme learning machines (ELMs) have gained acceptance owing to their high efficiency and outstanding generalization ability. As a key component of data preprocessing, feature selection methods can decrease the noise or irrelevant data for ELMs. However, ELMs still do not have their own practical feature selection method for their special mechanism. In this study, we proposed a feature selection method for the ELM, named FELM. The proposed algorithm achieves highly efficient dimensionality reduction due to the feature ranking strategy. The FELM can simultaneously complete the feature selection and classification processes. In addition, by incorporating a memorization&ndash;generalization kernel into the FELM, the nonlinear case of it is issued (called FKELM). The FKELM can achieve high classification accuracy and extensive generalization by applying the property of memorization of training data. According to the experimental results on different artificial and benchmark datasets, the proposed algorithms achieve significantly better classification accuracy and faster training than the other methods.

]]>Axioms doi: 10.3390/axioms11090443

Authors: Jeong-Gon Lee Samy Mostafa Jong-Il Baek Sang-Hyeon Han Kul Hur

The inclusion, the intersection and the union between cubic sets are each defined in two ways. From this point of view, we introduce the concepts of cubic subgroupoids, cubic ideals, cubic subgroups, and cubic congruences as two types, respectively, and discuss their various properties. In particular, we give a relationship between the set of all cubic normal subgroups of a group and all cubic congruences on the group.

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Authors: Rutwig Campoamor-Stursberg Francisco Oviaño García

With the help of symbolic computer packages, the study of the cohomological rigidity of real solvable Lie algebras of rank one with a maximal torus of derivations t and the eigenvalue spectrum spec(t)=1,k,k+1,&#8943;,n+k&minus;2 initiated in a previous work is continued for arbitrary values k&ge;2, obtaining new hierarchies of solvable rigid Lie algebras.

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Authors: Faizan Ahmad Khan

After the introduction of almost contraction due to Berinde, the branch of metric fixed point theory has attracted much attention in this direction, and various fixed point results have been proved for almost contractions via different approaches. In this paper, the results on existence and uniqueness of fixed points are proved employing almost contraction conditions in the framework of metric space endowed with binary relation. Finally, some examples are constructed, which substantiate the utility of the newly proved results.

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Authors: Bo Jiang Yongge Tian Ruixia Yuan

Given the linear matrix equation AXB=C, we partition it into the form A1X11B1+A1X12B2+A2X21B1+A2X22B2=C, and then pre- and post-multiply both sides of the equation by the four orthogonal projectors generated from the coefficient matrices A1, A1, B1, and B2 to obtain four reduced linear matrix equations. In this situation, each of the four reduced equations involves just one of the four unknown submatrices X11, X12, X21, and X22, respectively. In this paper, we study the relationships between the general solution of AXB=C and the general solutions of the four reduced equations using some highly selective matrix analysis tools in relation to ranks, ranges, and generalized inverses of matrices.

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Authors: Víctor Hugo Pacheco-Valencia Nodari Vakhania Frank Ángel Hernández-Mira José Alberto Hernández-Aguilar

The Traveling Salesman Problem (TSP) aims to find the shortest tour for a salesman who starts and ends in the same city and visits the remaining n&minus;1 cities exactly once. There are a number of common generalizations of the problem including the Multiple Traveling Salesman Problem (MTSP), where instead of one salesman, there are k salesmen and the same amount of individual tours are to be constructed. We consider the Euclidean version of the problem where the distances between the cities are calculated in two-dimensional Euclidean space. Both general the TSP and its Euclidean version are strongly NP-hard. Hence, approximation algorithms with a good practical behavior are of primary interest. We describe a general method for the solution of the Euclidean versions of the TSP (including MTSP) that yields approximation algorithms with a favorable practical behavior for large real-life instances. Our method creates special types of convex hulls, which serve as a basis for the constructions of our initial and intermediate partial solutions. Here, we overview three algorithms; one of them is for the bounded version of the MTSP. The proposed novel algorithm for the Euclidean TSP provides close-to-optimal solutions for some real-life instances.

]]>Axioms doi: 10.3390/axioms11090438

Authors: Ali Algarni

In this study, we introduce a new compounded model called the complementary Bell&ndash;Weibull model and use it to address the problem of a group acceptance sampling plan predicted on a truncated life test. The median lifespan is used as a quality index to obtain the design constraints, namely sample size and approval number, under a predefined consumer&#347; risk and test termination period. Additionally, two real data applications are presented, and unknown parameters are estimated using the maximum likelihood approach.

]]>Axioms doi: 10.3390/axioms11090437

Authors: Wenhui Zhang Peixin Ye Shuo Xing Xu Xu

We propose the Weak Rescaled Pure Super Greedy Algorithm (WRPSGA) for approximation with respect to a dictionary D in Hilbert space. The WRPSGA is simpler than some popular greedy algorithms. We show that the convergence rate of the RPSGA on the closure of the convex hull of the &mu;-coherent dictionary D is optimal. Then, we design the Rescaled Pure Super Greedy Learning Algorithm (RPSGLA) for kernel-based supervised learning. We prove that the convergence rate of the RPSGLA can be arbitrarily close to the best rate O(m&minus;1) under some mild assumptions.

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Authors: Emre Deniz Hasan Erbay Mustafa Coşar

The multi-label customer reviews classification task aims to identify the different thoughts of customers about the product they are purchasing. Due to the impact of the COVID-19 pandemic, customers have become more prone to shopping online. As a consequence, the amount of text data on e-commerce is continuously increasing, which enables new studies to be carried out and important findings to be obtained with more detailed analysis. Nowadays, e-commerce customer reviews are analyzed by both researchers and sector experts, and are subject to many sentiment analysis studies. Herein, an analysis of customer reviews is carried out in order to obtain more in-depth thoughts about the product, rather than engaging in emotion-based analysis. Initially, we form a new customer reviews dataset made up of reviews by Turkish consumers in order to perform the proposed analysis. The created dataset contains more than 50,000 reviews in three different categories, and each review has multiple labels according to the comments made by the customers. Later, we applied machine learning methods employed for multi-label classification to the dataset. Finally, we compared and analyzed the results we obtained using a diverse set of statistical metrics. As a result of our experimental studies, we found the Micro Precision 0.9157, Micro Recall 0.8837, Micro F1 Score 0.8925, and Hamming Loss 0.0278 to be the most successful approaches.

]]>Axioms doi: 10.3390/axioms11090435

Authors: Yuqiang Feng Qian Pan Jun Jiang

The terminal value problem of differential equations has an important application background. In this paper, we are concerned with the terminal value problem of a first-order differential equation. Some sufficient conditions are given to obtain the existence and uniqueness results of solutions to the problem. Firstly, some comparison lemmas are established; secondly, an iterative technique and fixed point method are used to set up the main results; Finally, an example is provided to illustrate the application of the main results.

]]>Axioms doi: 10.3390/axioms11090434

Authors: Maksim V. Kukushkin

In this paper, having introduced a convergence of a series on the root vectors in the Abel-Lidskii sense, we present a valuable application to the evolution equations. The main issue of the paper is an approach allowing us to principally broaden conditions imposed upon the second term of the evolution equation in the abstract Hilbert space. In this way, we come to the definition of the function of an unbounded non-selfadjoint operator. Meanwhile, considering the main issue we involve an additional concept that is a generalization of the spectral theorem for a non-selfadjoint operator.

]]>Axioms doi: 10.3390/axioms11090433

Authors: Hui Liu Guanghua Song

The traditional covering problem has two assumptions: &ldquo;all or nothing coverage&rdquo; and &ldquo;individual coverage&rdquo;. There are settings where the two assumptions may be unrealistic. In this research, we relax the two assumptions and study the cooperative covering facility location problem with demand uncertainty. Previous research on the covering problem has not considered cooperative covering under uncertain demand, particularly our approach to effectiveness maximization and offering full control of the conservatism of the model. We propose a cooperative covering model to maximize effectiveness, including the quality per dollar as a criterion. Then, the demand at each node is assumed to be uncertain, and the robust counterparts of the deterministic model are presented by considering the different degrees of conservatism of the robust solution. More importantly, the non-linear programming is transformed into equivalent linear programming by introducing auxiliary variables and using duality theory. The numerical examples show that the optimal location of the facility is affected by the protection level and the decision maker can make a trade-off between conservatism and effectiveness in an uncertain environment. Moreover, when the protection level is large, the objective function value makes a smaller sacrifice to get high robustness. In addition, two ways to measure the price of robustness are defined. The facility location decision can be made by evaluating the relative decrease in effectiveness compared to the nominal demand model or by evaluating the relative increase in effectiveness compared to the complete protection model.

]]>Axioms doi: 10.3390/axioms11090432

Authors: Peng Jiang Geng Wu Yi-Chung Hu Xue Zhang Yining Ren

Overseas students constitute the paramount talent resource for China, and, hence, overseas talent mobility prediction is crucial for the formulation of China&rsquo;s talent strategy. This study proposes a new model for predicting the number of students studying abroad and returning students, based on the grey system theory, owing to the limited data and uncertainty of the influencing factors. The proposed model introduces change-point detection to determine the number of modeling time points, based on the fractional-order grey prediction model. We employed a change-point detection method to find the change points for determining the model length, based on the principle of new information priority, and used a fractional order accumulated generating operation to construct a grey prediction model. The two real data sets, the annual number of students studying abroad and returning students, were employed to verify the superiority of the proposed model. The results showed that the proposed model outperformed other benchmark models. Furthermore, the proposed model has been employed to predict the tendencies of overseas talent mobility in China by 2025. Further, certain policy recommendations for China&rsquo;s talent strategy development have been proposed, based on the prediction results.

]]>Axioms doi: 10.3390/axioms11090431

Authors: Juan-De-Dios González-Hedström Juan-José Miñana Oscar Valero

The main purpose of this paper is to study the relationship between those functions that aggregate relaxed indistinguishability fuzzy relations with respect to a collection of t-norms and those functions that merge relaxed pseudo-metrics, extending the classical approach explored for pseudo-metrics and indistinguishability fuzzy relations. Special attention is paid to the distinguished class of SSI-relaxed indistinguishability fuzzy relations showing that functions merging this special type of relaxed indistinguishability fuzzy relations can be expressed through functions aggregating SSD-relaxed pseudo-metrics. Outstanding differences between those functions aggregating indistinguishability fuzzy relations and those that aggregate their counterpart separating points are shown.

]]>Axioms doi: 10.3390/axioms11090430

Authors: Siamak Pedrammehr Mahsa Hejazian Mohammad Reza Chalak Qazani Hadi Parvaz Sajjad Pakzad Mir Mohammad Ettefagh Adeel H. Suhail

The purpose of this research is to investigate different milling parameters for optimization to achieve the maximum rate of material removal with the minimum tool wear and surface roughness. In this study, a tool wear factor is specified to investigate tool wear parameters and the amount of material removed during machining, simultaneously. The second output parameter is surface roughness. The DOE technique is used to design the experiments and applied to the milling machine. The practical data is used to develop different mathematical models. In addition, a single-objective genetic algorithm (GA) is applied to numerate the optimal hyperparameters of the proposed adaptive network-based fuzzy inference system (ANFIS) to achieve the best possible efficiency. Afterwards, the multi-objective GA is employed to extract the optimum cutting parameters to reach the specified tool wear and the least surface roughness. The proposed method is developed under MATLAB using the practically extracted dataset and neural network. The optimization results revealed that optimum values for feed rate, cutting speed, and depth of cut vary from 252.6 to 256.9 (m/min), 0.1005 to 0.1431 (mm/rev tooth), and from 1.2735 to 1.3108 (mm), respectively.

]]>Axioms doi: 10.3390/axioms11090429

Authors: Tosiya Miyasita

We consider an equation with exponential nonlinearity under the Dirichlet boundary condition. For a one- or two-dimensional domain, a global solution has been obtained. In this paper, to extend the result to a higher dimensional case, we concentrate on the radial solutions in an annulus. First, we construct a time-local solution with an abstract theory of differential equations. Next, we show that decreasing energy exists in this problem. Finally, we establish a global solution for the sufficiently small initial value and parameter by Sobolev embedding and Poincar&eacute; inequalities together with some technical estimates. Moreover, when we take the smaller parameter, we prove that the global solution tends to zero as time goes to infinity.

]]>Axioms doi: 10.3390/axioms11090428

Authors: Alina Alb Lupaş

New results concerning fuzzy differential subordination theory are obtained in this paper using the operator denoted by Dz&minus;&lambda;L&alpha;n, previously introduced by applying the Riemann&ndash;Liouville fractional integral to the convex combination of well-known Ruscheweyh and S&#259;l&#259;gean differential operators. A new fuzzy subclass DLnF&delta;,&alpha;,&lambda; is defined and studied involving the operator Dz&minus;&lambda;L&alpha;n. Fuzzy differential subordinations are obtained considering functions from class DLnF&delta;,&alpha;,&lambda; and the fuzzy best dominants are also given. Using particular functions interesting corollaries are obtained and an example shows how the obtained results can be applied.

]]>Axioms doi: 10.3390/axioms11090427

Authors: Adis Puška Darko Božanić Miroslav Nedeljković Miljojko Janošević

The goal of this research was to find a selection of green suppliers (GSS) that will, in the best way, help agricultural producers to apply green agricultural production using uncertainty in decision making. In order to avoid the possibility of uncertainty in the expert decision making, Z-numbers were used together with the fuzzy LMAW (Logarithm Methodology of Additive Weights) method and fuzzy CRADIS (Compromise Ranking of Alternatives from Distance to Ideal Solution) method. By applying Z-numbers and the fuzzy LMAW method, the weighting coefficients of the criteria were determined, where the experts, in addition to the criteria ratings, also defined the degrees of certainty in the criteria ratings they gave. The obtained results indicated that the criteria related to price and qualities are the most important during the selection process. To select the best alternative, the CRADIS method modified with Z-numbers and fuzzy numbers was applied. The results obtained by applying this method showed that suppliers A2 and A3 have the best characteristics and are the first choice for the procurement of raw and production materials. As part of the paper, the validation of the results and the sensitivity analysis of the model were carried out by conducting the procedure of comparing the obtained results with the results obtained by other MCDM methods and changing the weighting coefficients of the criteria. These analyses indicated that the model presented provides stable results. The conducted research showed how Z-numbers can be used to reduce uncertainty in decision making and how Z-numbers can be used with other fuzzy methods to perform GSS.

]]>Axioms doi: 10.3390/axioms11090426

Authors: Tamara Antonova Roman Dmytryshyn Roman Kurka

The paper deals with the problem of expansion of the ratios of the confluent hypergeometric function of N variables &Phi;D(N)(a,b&macr;;c;z&macr;) into the branched continued fractions (BCF) of the general form with N branches of branching and investigates the convergence of these BCF. The algorithms of construction for BCF expansions of confluent hypergeometric function &Phi;D(N) ratios are based on some given recurrence relations for this function. The case of nonnegative parameters a,b1,&hellip;,bN&minus;1 and positive c is considered. Some convergence criteria for obtained BCF with elements in RN and CN are established. It is proven that these BCF converge to the functions which are an analytic continuation of the above-mentioned ratios of function &Phi;D(N)(a,b&macr;;c;z&macr;) in some domain of CN.

]]>Axioms doi: 10.3390/axioms11090425

Authors: Susmit Bagchi

The topological views of a measure space provide deep insights. In this paper, the sigma-set algebraic structure is extended in a Hausdorff topological space based on the locally compactable neighborhood systems without considering strictly (metrized) Borel variety. The null extension gives rise to a quasi sigma-semiring based on sigma-neighborhoods, which are rectifiable in view of Dieudonn&eacute; measure in n-space. The concepts of symmetric signed measure, uniformly pushforward measure, and its interval-valued Lebesgue variety within a topological measure space are introduced. The symmetric signed measure preserves the total ordering on the real line; however, the collapse of symmetry admits Dieudonn&eacute; measure within the topological space. The locally constant measures in compact supports in sigma-neighborhood systems are invariant under topological deformation retraction in a simply connected space where the sequence of deformation retractions induces a strongly convergent sequence of measures. Moreover, the extended sigma-structures in an automorphic and isomorphic topological space preserve the properties of uniformly pushforward measure. The Haar-measurable group algebraic structures equivalent to additive integer groups arise under the locally constant and signed measures as long as the topological space is non-compact and the null-extended sigma-neighborhood system admits compact groups. The comparative analyses of the proposed concepts with respect to existing results are outlined.

]]>Axioms doi: 10.3390/axioms11090424

Authors: İbrahim Gürler Ozan Çakır Bora Gündüzyeli

In this manuscript, with grounding in Liu&ndash;Lin axioms of greyness degree and information content, we provide new results that relate to these concepts in consideration of a number of mathematical operations over a sequence of grey numbers. In particular, we derive greyness degree results of summation, conic combination, and convex combination of a sequence, as well as inverse of a number and normalization of a number over a sequence. Then, we turn our attention to prove information content results for the union and intersection of a sequence. We illustrate our results by using a simple Monte Carlo simulation in the multi-attribute decision-making context, and by using an interesting dice-rolling experiment. Through our analysis, we also provide some new definitions, such as for conic combination, convex combination, normalization, and union and intersection operations. The novelty of the derived results in this study is that they can help researchers and practitioners of grey systems in tracking probable intensifications and reductions in the greyness degree in successive application steps of their working methods. Moreover, researchers are provided with two results to calculate information content for the union and intersection of grey numbers in an uncomplicated manner.

]]>Axioms doi: 10.3390/axioms11090423

Authors: Mahmoud El-Morshedy Mohammed H. El-Menshawy Mohammed M. A. Almazah Rashad M. El-Sagheer Mohamed S. Eliwa

In this paper, the effect of fuzzy time series on estimates of the spectral, bispectral and normalized bispectral density functions are studied. This study is conducted for one of the integer autoregressive of order one (INAR(1)) models. The model of interest here is the dependent counting geometric INAR(1) which is symbolized by (DCGINAR(1)). A realization is generated for this model of size n = 500 for estimation. Based on fuzzy time series, the forecasted observations of this model are obtained. The estimators of spectral, bispectral and normalized bispectral density functions are smoothed by different one- and two-dimensional lag windows. Finally, after the smoothing, all estimators are studied in the case of generated and forecasted observations of the DCGINAR(1) model. We investigate the contribution of the fuzzy time series to the smoothing of these estimates through the results.

]]>Axioms doi: 10.3390/axioms11080422

Authors: Aníbal Coronel Fernando Huancas Esperanza Lozada Alex Tello

In this article, we propose a one-dimensional heat conduction model for a double-pane window with a temperature-jump boundary condition and a thermal lagging interfacial effect condition between layers. We construct a second-order accurate finite difference scheme to solve the heat conduction problem. The designed scheme is mainly based on approximations satisfying the facts that all inner grid points has second-order temporal and spatial truncation errors, while at the boundary points and at inter-facial points has second-order temporal truncation error and first-order spatial truncation error, respectively. We prove that the finite difference scheme introduced is unconditionally stable, convergent, and has a rate of convergence two in space and time for the L&infin;-norm. Moreover, we give a numerical example to confirm our theoretical results.

]]>Axioms doi: 10.3390/axioms11080421

Authors: Yufen Wei Yu Li

This paper considers the time taken for young predators to become adult predators as the delay and constructs a stage-structured predator&ndash;prey system with Holling III response and time delay. Using the persistence theory for infinite-dimensional systems and the Hurwitz criterion, the permanent persistence condition of this system and the local stability condition of the system&rsquo;s coexistence equilibrium are given. Further, it is proven that the system undergoes a Hopf bifurcation at the coexistence equilibrium. By using Lyapunov functions and the LaSalle invariant principle, it is shown that the trivial equilibrium and the coexistence equilibrium are globally asymptotically stable, and sufficient conditions are derived for the global stability of the coexistence equilibrium. Some numerical simulations are carried out to illustrate the main results.

]]>Axioms doi: 10.3390/axioms11080420

Authors: Songsong Dai

This paper investigates the pointwise comparability of overlap and grouping functions which obtained by Bustince et al.&rsquo;s and Bedregal et al.&rsquo;s generator pairs, respectively. Some necessary and sufficient conditions for the comparison of these functions are proved. We also introduce some compositions of these functions and study the order preservation of these compositions.

]]>Axioms doi: 10.3390/axioms11080419

Authors: Minxia Luo Wenling Li Hongyan Shi

Two important basic inference models of fuzzy reasoning are Fuzzy Modus Ponens (FMP) and Fuzzy Modus Tollens (FMT). In order to solve FMP and FMT problems, the full implication triple I algorithm, the reverse triple I algorithm and the Subsethood Inference Subsethood (SIS for short) algorithm are proposed, respectively. Furthermore, the existing reasoning algorithms are extended to intuitionistic fuzzy sets and interval-valued fuzzy sets according to different needs. The purpose of this paper is to study the relationship between intuitionistic fuzzy reasoning algorithms and interval-valued fuzzy reasoning algorithms. It is proven that there is a bijection between the solutions of intuitionistic fuzzy triple I algorithm and the interval-valued fuzzy triple I algorithm. Then, there is a bijection between the solutions of intuitionistic fuzzy reverse triple I algorithm and the interval-valued fuzzy reverse triple I algorithm. At the same time, it is shown that there is also a bijection between the solutions of intuitionistic fuzzy SIS algorithm and interval-valued fuzzy SIS algorithm.

]]>Axioms doi: 10.3390/axioms11080418

Authors: Fangdi Wang Zengtai Gong Yabin Shao

As is well known, complex intuitionistic fuzzy preference relation can describe the fuzzy characters of things in more detail and comprehensively and is very useful in dealing with decision-making problems that include periodic or recurring phenomena. However, sometimes, a decision-maker may provide incomplete judgments in a complex intuitionistic fuzzy preference relation because of a lack of knowledge, time pressure, and the decision-makers&rsquo; limited expertise related to the problem domain. In such cases, it would be sensible not to force the expert to express &ldquo;false&rdquo; preferences over these objects. Consequently, how to define incomplete complex intuitionistic fuzzy preference relations and to estimate their missing elements in an incomplete complex intuitionistic fuzzy preference relation becomes a necessary step in a decision-making process. In this paper, the concept of incomplete complex intuitionistic fuzzy preference relation is introduced and its properties are discussed. Meanwhile, the multiplicative consistent incomplete complex intuitionistic fuzzy preference relations are defined. Secondly, estimating algorithms are developed to estimate the missing elements in the acceptable incomplete complex intuitionistic fuzzy preference relations. Finally, an expert weight determination algorithm and the group decision-making algorithms based on incomplete complex intuitionistic fuzzy preference relations are established. The solving process of the algorithms is illustrated by an example, the practicability of the algorithms is verified, the advantages and disadvantages of two group decision-making algorithms are compared and analyzed, and the simulation verification of incomplete complex intuitionistic fuzzy system is carried out by MATLAB software. The framework proposed in this paper effectively generalizes and enriches the previous works and has a good application prospect.

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