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Symmetry, Volume 9, Issue 11 (November 2017)

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Cover Story (view full-size image) CPT and Lorentz symmetry are generally assumed to hold exactly in nature. The possibility of their [...] Read more.
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Open AccessArticle Analytical Treatment of Higher-Order Graphs: A Path Ordinal Method for Solving Graphs
Symmetry 2017, 9(11), 288; https://doi.org/10.3390/sym9110288
Received: 13 October 2017 / Revised: 17 November 2017 / Accepted: 17 November 2017 / Published: 22 November 2017
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Abstract
Analytical treatment of the composition of higher-order graphs representing linear relations between variables is developed. A path formalism to deal with problems in graph theory is introduced. It is shown how paths in the composed graph representing individual contributions to variables relation can
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Analytical treatment of the composition of higher-order graphs representing linear relations between variables is developed. A path formalism to deal with problems in graph theory is introduced. It is shown how paths in the composed graph representing individual contributions to variables relation can be enumerated and represented by ordinals. The method allows for one to extract partial information and gives an alternative to classical graph approach. Full article
(This article belongs to the Special Issue Graph Theory)
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Open AccessArticle The Choice of Gadolinium-Based Contrast Agents: A Radiologist’s Responsibility between Pharmaceutical Equivalence and Bioethical Issues
Symmetry 2017, 9(11), 287; https://doi.org/10.3390/sym9110287
Received: 24 October 2017 / Revised: 14 November 2017 / Accepted: 17 November 2017 / Published: 22 November 2017
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Abstract
Contrast Agents (CA) are among the most commonly prescribed drugs worldwide, and are used, with a variety of techniques, to increase and intensify the differences between body tissues and to help radiologist make diagnoses in a fast and precise way. In recent decades,
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Contrast Agents (CA) are among the most commonly prescribed drugs worldwide, and are used, with a variety of techniques, to increase and intensify the differences between body tissues and to help radiologist make diagnoses in a fast and precise way. In recent decades, advancements in research have resulted in significant improvements in their composition, and have made them safer and better-tolerated by patients; this notwithstanding, although the currently available CA are generally considered to be safe, their use is not completely without risk. The use of CA faces the radiologist with economic considerations, bioethical dilemmas, and possible profiles of professional responsibility. In fact, to achieve the best results in diagnostic imaging, radiologists have to focus on making an appropriate choice of CA, in consideration of efficacy, safety and appropriateness. Moreover, besides by cost/benefit models widely introduced in health management, radiologists are also influenced by their responsibility of appropriate use for the various diagnostic tests and, finally, the choice of best CA to utilise for each individual patient. Thus, the dilemma of choosing between the best and the most cost-effective tests and procedures is occurring more frequently every day. Different variables, such as the patient, examinations, and technology available, can affect the choice of CA in terms of obtaining the highest diagnostic quality, minimum impact on higher-risk patients, and optimisation of used volumes and injection flows. Full article
(This article belongs to the Special Issue Medical Imaging and Imaging Modalities)
Open AccessArticle Fishmeal Supplier Evaluation and Selection for Aquaculture Enterprise Sustainability with a Fuzzy MCDM Approach
Symmetry 2017, 9(11), 286; https://doi.org/10.3390/sym9110286
Received: 29 October 2017 / Revised: 11 November 2017 / Accepted: 14 November 2017 / Published: 21 November 2017
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Abstract
In the aquaculture industry, feed that is of poor quality or nutritionally imbalanced can cause problems including low weight, poor growth, poor palatability, and increased mortality, all of which can induce a decrease in aquaculture production. Fishmeal is considered a better source of
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In the aquaculture industry, feed that is of poor quality or nutritionally imbalanced can cause problems including low weight, poor growth, poor palatability, and increased mortality, all of which can induce a decrease in aquaculture production. Fishmeal is considered a better source of protein and its addition as an ingredient in the aquafeed makes aquatic animals grow fast and healthy. This means that fishmeal is the most important feed ingredient in aquafeed for the aquaculture industry. For the aquaculture industry in Taiwan, about 144,000 ton/USD $203,245,000 of fishmeal was imported, mostly from Peru, in 2016. Therefore, the evaluation and selection of fishmeal suppliers is a very important part of the decision-making process for a Taiwanese aquaculture enterprise. This study constructed a multiple criteria decision-making evaluation model for the selection of fishmeal suppliers using the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) approach based on the weights obtained with the entropy method in a fuzzy decision-making environment. This hybrid approach could effectively and conveniently measure the comprehensive performance of the main Peruvian fishmeal suppliers for practical applications. In addition, the results and processes described herein function as a good reference for an aquaculture enterprise in making decisions when purchasing fishmeal. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making) Printed Edition available
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Open AccessArticle Optimized Charging Scheduling with Single Mobile Charger for Wireless Rechargeable Sensor Networks
Symmetry 2017, 9(11), 285; https://doi.org/10.3390/sym9110285
Received: 7 October 2017 / Revised: 15 November 2017 / Accepted: 16 November 2017 / Published: 21 November 2017
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Abstract
Due to the rapid development of wireless charging technology, the recharging issue in wireless rechargeable sensor network (WRSN) has been a popular research problem in the past few years. The weakness of previous work is that charging route planning is not reasonable. In
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Due to the rapid development of wireless charging technology, the recharging issue in wireless rechargeable sensor network (WRSN) has been a popular research problem in the past few years. The weakness of previous work is that charging route planning is not reasonable. In this work, a dynamic optimal scheduling scheme aiming to maximize the vacation time ratio of a single mobile changer for WRSN is proposed. In the proposed scheme, the wireless sensor network is divided into several sub-networks according to the initial topology of deployed sensor networks. After comprehensive analysis of energy states, working state and constraints for different sensor nodes in WRSN, we transform the optimized charging path problem of the whole network into the local optimization problem of the sub networks. The optimized charging path with respect to dynamic network topology in each sub-network is obtained by solving an optimization problem, and the lifetime of the deployed wireless sensor network can be prolonged. Simulation results show that the proposed scheme has good and reliable performance for a small wireless rechargeable sensor network. Full article
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Open AccessArticle Granular Structure of Type-2 Fuzzy Rough Sets over Two Universes
Symmetry 2017, 9(11), 284; https://doi.org/10.3390/sym9110284
Received: 24 October 2017 / Revised: 14 November 2017 / Accepted: 15 November 2017 / Published: 21 November 2017
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Abstract
Granular structure plays a very important role in the model construction, theoretical analysis and algorithm design of a granular computing method. The granular structures of classical rough sets and fuzzy rough sets have been proven to be clear. In classical rough set theory,
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Granular structure plays a very important role in the model construction, theoretical analysis and algorithm design of a granular computing method. The granular structures of classical rough sets and fuzzy rough sets have been proven to be clear. In classical rough set theory, equivalence classes are basic granules, and the lower and upper approximations of a set can be computed by those basic granules. In the theory of fuzzy rough set, granular fuzzy sets can be used to describe the lower and upper approximations of a fuzzy set. This paper discusses the granular structure of type-2 fuzzy rough sets over two universes. Definitions of type-2 fuzzy rough sets over two universes are given based on a wavy-slice representation of type-2 fuzzy sets. Two granular type-2 fuzzy sets are deduced and then proven to be basic granules of type-2 fuzzy rough sets over two universes. Then, the properties of lower and upper approximation operators and these two granular type-2 fuzzy sets are investigated. At last, several examples are given to show the applications of type-2 fuzzy rough sets over two universes. Full article
(This article belongs to the Special Issue Fuzzy Sets Theory and Its Applications)
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Open AccessArticle Hierarchical Meta-Learning in Time Series Forecasting for Improved Interference-Less Machine Learning
Symmetry 2017, 9(11), 283; https://doi.org/10.3390/sym9110283
Received: 24 October 2017 / Revised: 1 November 2017 / Accepted: 1 November 2017 / Published: 18 November 2017
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Abstract
The importance of an interference-less machine learning scheme in time series prediction is crucial, as an oversight can have a negative cumulative effect, especially when predicting many steps ahead of the currently available data. The on-going research on noise elimination in time series
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The importance of an interference-less machine learning scheme in time series prediction is crucial, as an oversight can have a negative cumulative effect, especially when predicting many steps ahead of the currently available data. The on-going research on noise elimination in time series forecasting has led to a successful approach of decomposing the data sequence into component trends to identify noise-inducing information. The empirical mode decomposition method separates the time series/signal into a set of intrinsic mode functions ranging from high to low frequencies, which can be summed up to reconstruct the original data. The usual assumption that random noises are only contained in the high-frequency component has been shown not to be the case, as observed in our previous findings. The results from that experiment reveal that noise can be present in a low frequency component, and this motivates the newly-proposed algorithm. Additionally, to prevent the erosion of periodic trends and patterns within the series, we perform the learning of local and global trends separately in a hierarchical manner which succeeds in detecting and eliminating short/long term noise. The algorithm is tested on four datasets from financial market data and physical science data. The simulation results are compared with the conventional and state-of-the-art approaches for time series machine learning, such as the non-linear autoregressive neural network and the long short-term memory recurrent neural network, respectively. Statistically significant performance gains are recorded when the meta-learning algorithm for noise reduction is used in combination with these artificial neural networks. For time series data which cannot be decomposed into meaningful trends, applying the moving average method to create meta-information for guiding the learning process is still better than the traditional approach. Therefore, this new approach is applicable to the forecasting of time series with a low signal to noise ratio, with a potential to scale adequately in a multi-cluster system due to the parallelized nature of the algorithm. Full article
(This article belongs to the Special Issue Novel Machine Learning Approaches for Intelligent Big Data)
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Open AccessArticle An Appraisal Model Based on a Synthetic Feature Selection Approach for Students’ Academic Achievement
Symmetry 2017, 9(11), 282; https://doi.org/10.3390/sym9110282
Received: 14 October 2017 / Revised: 11 November 2017 / Accepted: 13 November 2017 / Published: 18 November 2017
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Abstract
Obtaining necessary information (and even extracting hidden messages) from existing big data, and then transforming them into knowledge, is an important skill. Data mining technology has received increased attention in various fields in recent years because it can be used to find historical
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Obtaining necessary information (and even extracting hidden messages) from existing big data, and then transforming them into knowledge, is an important skill. Data mining technology has received increased attention in various fields in recent years because it can be used to find historical patterns and employ machine learning to aid in decision-making. When we find unexpected rules or patterns from the data, they are likely to be of high value. This paper proposes a synthetic feature selection approach (SFSA), which is combined with a support vector machine (SVM) to extract patterns and find the key features that influence students’ academic achievement. For verifying the proposed model, two databases, namely, “Student Profile” and “Tutorship Record”, were collected from an elementary school in Taiwan, and were concatenated into an integrated dataset based on students’ names as a research dataset. The results indicate the following: (1) the accuracy of the proposed feature selection approach is better than that of the Minimum-Redundancy-Maximum-Relevance (mRMR) approach; (2) the proposed model is better than the listing methods when the six least influential features have been deleted; and (3) the proposed model can enhance the accuracy and facilitate the interpretation of the pattern from a hybrid-type dataset of students’ academic achievement. Full article
(This article belongs to the Special Issue Information Technology and Its Applications)
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Open AccessArticle Time Series Seasonal Analysis Based on Fuzzy Transforms
Symmetry 2017, 9(11), 281; https://doi.org/10.3390/sym9110281
Received: 27 September 2017 / Revised: 23 October 2017 / Accepted: 11 November 2017 / Published: 17 November 2017
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Abstract
We define a new seasonal forecasting method based on fuzzy transforms. We use the best interpolating polynomial for extracting the trend of the time series and generate the inverse fuzzy transform on each seasonal subset of the universe of discourse for predicting the
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We define a new seasonal forecasting method based on fuzzy transforms. We use the best interpolating polynomial for extracting the trend of the time series and generate the inverse fuzzy transform on each seasonal subset of the universe of discourse for predicting the value of an assigned output. In the first example, we use the daily weather dataset of the municipality of Naples (Italy) starting from data collected from 2003 to 2015 making predictions on mean temperature, max temperature and min temperature, all considered daily. In the second example, we use the daily mean temperature measured at the weather station “Chiavari Caperana” in the Liguria Italian Region. We compare the results with our method, the average seasonal variation, Auto Regressive Integrated Moving Average (ARIMA) and the usual fuzzy transforms concluding that the best results are obtained under our approach in both examples. In addition, the comparison results show that, for seasonal time series that have no consistent irregular variations, the performance obtained with our method is comparable with the ones obtained using Support Vector Machine- and Artificial Neural Networks-based models. Full article
(This article belongs to the Special Issue Symmetry in Fuzzy Sets and Systems)
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Open AccessArticle How Objective a Neutral Word Is? A Neutrosophic Approach for the Objectivity Degrees of Neutral Words
Symmetry 2017, 9(11), 280; https://doi.org/10.3390/sym9110280
Received: 9 October 2017 / Revised: 12 November 2017 / Accepted: 15 November 2017 / Published: 17 November 2017
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Abstract
In the latest studies concerning the sentiment polarity of words, the authors mostly consider the positive and negative constructions, without paying too much attention to the neutral words, which can have, in fact, significant sentiment degrees. More precisely, not all the neutral words
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In the latest studies concerning the sentiment polarity of words, the authors mostly consider the positive and negative constructions, without paying too much attention to the neutral words, which can have, in fact, significant sentiment degrees. More precisely, not all the neutral words have zero positivity or negativity scores, some of them having quite important nonzero scores for these polarities. At this moment, in the literature, a word is considered neutral if its positive and negative scores are equal, which implies two possibilities: (1) zero positive and negative scores; (2) nonzero, but equal positive and negative scores. It is obvious that these cases represent two different categories of neutral words that must be treated separately by a sentiment analysis task. In this paper, we present a comprehensive study about the neutral words applied to English as is developed with the aid of SentiWordNet 3.0: the publicly available lexical resource for opinion mining. We designed our study in order to provide an accurate classification of the so-called “neutral words” described in terms of sentiment scores and using measures from neutrosophy theory. The intended scope is to fill the gap concerning the neutrality aspect by giving precise measurements for the words’ objectivity. Full article
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Open AccessArticle Novel Integrated Multi-Criteria Model for Supplier Selection: Case Study Construction Company
Symmetry 2017, 9(11), 279; https://doi.org/10.3390/sym9110279
Received: 12 October 2017 / Revised: 4 November 2017 / Accepted: 9 November 2017 / Published: 17 November 2017
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Abstract
Supply chain presents a very complex field involving a large number of participants. The aim of the complete supply chain is finding an optimum from the aspect of all participants, which is a rather complex task. In order to ensure optimum satisfaction for
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Supply chain presents a very complex field involving a large number of participants. The aim of the complete supply chain is finding an optimum from the aspect of all participants, which is a rather complex task. In order to ensure optimum satisfaction for all participants, it is necessary that the beginning phase consists of correct evaluations and supplier selection. In this study, the supplier selection was performed in the construction company, on the basis of a new approach in the field of multi-criteria model. Weight coefficients were obtained by DEMATEL (Decision Making Trial and Evaluation Laboratory) method, based on the rough numbers. Evaluation and the supplier selection were made on the basis of a new Rough EDAS (Evaluation based on Distance from Average Solution) method, which presents one of the latest methods in this field. In order to determine the stability of the model and the applicability of the proposed Rough EDAS method, an extension of the COPRAS and MULTIMOORA method by rough numbers was also performed in this study, and the findings of the comparative analysis were presented. Besides the new approaches based on the extension by rough numbers, the results are also compared with the Rough MABAC (MultiAttributive Border Approximation area Comparison) and Rough MAIRCA (MultiAttributive Ideal-Real Comparative Analysis). In addition, in the sensitivity analysis, 18 different scenarios were formed, the ones in which criteria change their original values. At the end of the sensitivity analysis, SCC (Spearman Correlation Coefficient) of the obtained ranges was carried out, confirming the applicability of the proposed approaches. Full article
(This article belongs to the Special Issue Civil Engineering and Symmetry)
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Open AccessArticle Conflicting Information Fusion Based on an Improved DS Combination Method
Symmetry 2017, 9(11), 278; https://doi.org/10.3390/sym9110278
Received: 30 October 2017 / Revised: 14 November 2017 / Accepted: 15 November 2017 / Published: 16 November 2017
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Abstract
An effective and reliable fusion method for conflicting information is proposed in this paper. Compared with a single-sensor system, a multi-sensor fusion system can comprehensively combine the redundancy and complementarity of multi-sensor information to obtain better system performance. Hence, the multi-sensor fusion system
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An effective and reliable fusion method for conflicting information is proposed in this paper. Compared with a single-sensor system, a multi-sensor fusion system can comprehensively combine the redundancy and complementarity of multi-sensor information to obtain better system performance. Hence, the multi-sensor fusion system has become one of the research hotspots. However, due to lack knowledge about the measurement environment and limited sensor accuracy, the multi-sensor system inevitably appears to have imperfect, uncertain and inconsistent information. To solve the problem, we introduce one powerful uncertainty reasoning method: Dempster–Shafer theory (DS theory). With convincing measurement and a forceful combination of uncertain information, DS theory is widely applied in various fields, like decision-making, expert systems, target tracking, monitoring systems, etc. Nevertheless, DS theory will produce counter-intuitive fusion results when the pieces of evidence are highly conflicting. To address this issue, we raise an improved DS combination method for conflicting information fusion in this paper. First of all, the modified Minkowski distance function and the betting-commitment distance function are separately employed to revise potentially conflicting pieces of evidence. The procedure availably solves the conflicting situations caused by unreliable and imprecise evidence sources, which enhances the consistency among pieces of evidence. Then, based on two revised pieces of evidence, a conflicting redistribution strategy based on locally conflicting analyses is put forward. The approach dexterously combines two revised pieces of evidence to avoid conflicting situations caused by compulsive normalization, which further improves the accuracy and convergence speed of the multi-sensor fusion system. Finally, two experimental analyses with consistent information and conflicting information reveal the remarkable effectiveness and priority of the proposed algorithm for the multi-sensor fusion system. Consequently, this paper has certain value for the multi-sensor fusion system. Full article
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Open AccessArticle Malignant and Benign Mass Segmentation in Mammograms Using Active Contour Methods
Symmetry 2017, 9(11), 277; https://doi.org/10.3390/sym9110277
Received: 1 October 2017 / Revised: 10 November 2017 / Accepted: 12 November 2017 / Published: 16 November 2017
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Abstract
The correct segmentation of tumours can simplify formulate the diagnostic hypothesis, particularly in cases of irregular shapes, with fuzzy margins or spicules growing into the surrounding tissue, which are more likely to be malignant. In this study, the following active contour methods were
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The correct segmentation of tumours can simplify formulate the diagnostic hypothesis, particularly in cases of irregular shapes, with fuzzy margins or spicules growing into the surrounding tissue, which are more likely to be malignant. In this study, the following active contour methods were used to segment the masses: an edge–based active contour model using an inflation/deflation force with a damping coefficient (EM), a geometric active contour model (GAC) and an active contour without edges (ACWE). The preprocessing techniques presented in this publication are to reduce noise and at the same time amplify uniform areas of images in order to improve segmentation results. In addition, the use of image sampling by bicubic interpolation was tested to shorten the evolution time of active contour methods. The experiments used a test set composed of 100 cases taken from two publicly available databases: Digital Database for Screening Mammography (DDSM) and Mammographic Image Analysis Society (MIAS) database. The qualitative assessment concerned the ability to formulate an adequate diagnostic hypothesis and, for the individual methods (malignant and benign cases together), it amounted to at least: 81% (EM), 76% (GAC), and 69% (ACWE). The quantitative test consisted of measuring the following indexes: overlap value (OV) and extra fraction (EF). The OV of the segmentation for malignant and benign cases had the following average values: 0.81 ∓ 0.10 (EM), 0.79 ∓ 0.09 (GAC), 0.76 ∓ 0.18 (ACWE). The average values of the EF index, in turn, amounted to: 0.07 ∓ 0.06 (EM), 0.07 ∓ 0.05 (GAC) 0.34 ∓ 0.32 (ACWE). The qualitative and quantitative results obtained are the best for EM and are comparable or better than for other methods presented in the literature. Full article
(This article belongs to the Special Issue Advances in Medical Image Segmentation)
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Open AccessArticle Retinal Vessel Segmentation via Structure Tensor Coloring and Anisotropy Enhancement
Symmetry 2017, 9(11), 276; https://doi.org/10.3390/sym9110276
Received: 23 October 2017 / Revised: 9 November 2017 / Accepted: 10 November 2017 / Published: 14 November 2017
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Abstract
Retinal vessel segmentation is one of the preliminary tasks for developing diagnosis software systems related to various retinal diseases. In this study, a fully automated vessel segmentation system is proposed. Firstly, the vessels are enhanced using a Frangi Filter. Afterwards, Structure Tensor is
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Retinal vessel segmentation is one of the preliminary tasks for developing diagnosis software systems related to various retinal diseases. In this study, a fully automated vessel segmentation system is proposed. Firstly, the vessels are enhanced using a Frangi Filter. Afterwards, Structure Tensor is applied to the response of the Frangi Filter and a 4-D tensor field is obtained. After decomposing the Eigenvalues of the tensor field, the anisotropy between the principal Eigenvalues are enhanced exponentially. Furthermore, this 4-D tensor field is converted to the 3-D space which is composed of energy, anisotropy and orientation and then a Contrast Limited Adaptive Histogram Equalization algorithm is applied to the energy space. Later, the obtained energy space is multiplied by the enhanced mean surface curvature of itself and the modified 3-D space is converted back to the 4-D tensor field. Lastly, the vessel segmentation is performed by using Otsu algorithm and tensor coloring method which is inspired by the ellipsoid tensor visualization technique. Finally, some post-processing techniques are applied to the segmentation result. In this study, the proposed method achieved mean sensitivity of 0.8123, 0.8126, 0.7246 and mean specificity of 0.9342, 0.9442, 0.9453 as well as mean accuracy of 0.9183, 0.9442, 0.9236 for DRIVE, STARE and CHASE_DB1 datasets, respectively. The mean execution time of this study is 6.104, 6.4525 and 18.8370 s for the aforementioned three datasets respectively. Full article
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Open AccessArticle Neutrosophic Duplet Semi-Group and Cancellable Neutrosophic Triplet Groups
Symmetry 2017, 9(11), 275; https://doi.org/10.3390/sym9110275
Received: 14 October 2017 / Revised: 9 November 2017 / Accepted: 10 November 2017 / Published: 14 November 2017
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Abstract
The notions of the neutrosophic triplet and neutrosophic duplet were introduced by Florentin Smarandache. From the existing research results, the neutrosophic triplets and neutrosophic duplets are completely different from the classical algebra structures. In this paper, we further study neutrosophic duplet sets, neutrosophic
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The notions of the neutrosophic triplet and neutrosophic duplet were introduced by Florentin Smarandache. From the existing research results, the neutrosophic triplets and neutrosophic duplets are completely different from the classical algebra structures. In this paper, we further study neutrosophic duplet sets, neutrosophic duplet semi-groups, and cancellable neutrosophic triplet groups. First, some new properties of neutrosophic duplet semi-groups are funded, and the following important result is proven: there is no finite neutrosophic duplet semi-group. Second, the new concepts of weak neutrosophic duplet, weak neutrosophic duplet set, and weak neutrosophic duplet semi-group are introduced, some examples are given by using the mathematical software MATLAB (MathWorks, Inc., Natick, MA, USA), and the characterizations of cancellable weak neutrosophic duplet semi-groups are established. Third, the cancellable neutrosophic triplet groups are investigated, and the following important result is proven: the concept of cancellable neutrosophic triplet group and group coincide. Finally, the neutrosophic triplets and weak neutrosophic duplets in BCI-algebras are discussed. Full article
(This article belongs to the Special Issue Neutrosophic Theories Applied in Engineering)
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Open AccessFeature PaperArticle Operations on Oriented Maps
Symmetry 2017, 9(11), 274; https://doi.org/10.3390/sym9110274
Received: 31 July 2017 / Revised: 7 November 2017 / Accepted: 11 November 2017 / Published: 14 November 2017
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Abstract
A map on a closed surface is a two-cell embedding of a finite connected graph. Maps on surfaces are conveniently described by certain trivalent graphs, known as flag graphs. Flag graphs themselves may be considered as maps embedded in the same surface as
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A map on a closed surface is a two-cell embedding of a finite connected graph. Maps on surfaces are conveniently described by certain trivalent graphs, known as flag graphs. Flag graphs themselves may be considered as maps embedded in the same surface as the original graph. The flag graph is the underlying graph of the dual of the barycentric subdivision of the original map. Certain operations on maps can be defined by appropriate operations on flag graphs. Orientable surfaces may be given consistent orientations, and oriented maps can be described by a generating pair consisting of a permutation and an involution on the set of arcs (or darts) defining a partially directed arc graph. In this paper we describe how certain operations on maps can be described directly on oriented maps via arc graphs. Full article
(This article belongs to the Special Issue Polyhedral Structures) Printed Edition available
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