Symmetry

Research

18 pages, 1127 KiB

Open AccessFeature PaperArticle

The Fuzzified Natural Transformation between Categorial Functors and Its Selected Categorial Aspects

by Krystian Jobczyk

Symmetry 2020, 12(9), 1578; https://doi.org/10.3390/sym12091578 - 22 Sep 2020

Cited by 1 | Viewed by 2501

The natural transformation constitutes one of the most important entity of category theory and it introduces a piece of sophisticated dynamism to the categorial structures. Each natural transformation forms a unique mapping between the so-called functors, which live between categories. In the most [...] Read more.

The natural transformation constitutes one of the most important entity of category theory and it introduces a piece of sophisticated dynamism to the categorial structures. Each natural transformation forms a unique mapping between the so-called functors, which live between categories. In the most simple contexts, natural transformations may be recognized by commutativity of diagrams, which determine them. In fact, the natural transformation does not form any single mapping, but a pair of two components, which–together with the commutativity condition itself–introduces a kind of a symmetry to the functor diagrams. Meanwhile, the general form of the natural transformation may be predicted by means the so-called Yoneda’s lemma in each scenario based on two-valued logic. Meanwhile, the situation may be radically different if we deal with multi-diagrams (instead of the single ones) and if we exchange the two-valued scenario for a multi-valued or fuzzy one. Due to this background–the paper introduces a new concept of multi-fuzzy natural transformation. Its definition exploits the notion of fuzzy natural transformation. Moreover, a multi-fuzzy Yoneda’s lemma is formulated and proved. Finally, some references of these constructions to coding theory are elucidated in last parts of the paper. Full article

(This article belongs to the Special Issue Fuzzy Mathematics Applied to Science, Engineering and Sustainability Issues)

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19 pages, 2960 KiB

Open AccessArticle

Graph Learning-Based Ontology Sparse Vector Computing

by Jianzhang Wu, Arun Kumar Sangaiah and Wei Gao

Symmetry 2020, 12(9), 1562; https://doi.org/10.3390/sym12091562 - 21 Sep 2020

Cited by 2 | Viewed by 2768

Abstract

The ontology sparse vector learning algorithm is essentially a dimensionality reduction trick, i.e., the key components in the p-dimensional vector are taken out, and the remaining components are set to zero, so as to obtain the key information in a certain ontology [...] Read more.

The ontology sparse vector learning algorithm is essentially a dimensionality reduction trick, i.e., the key components in the p-dimensional vector are taken out, and the remaining components are set to zero, so as to obtain the key information in a certain ontology application background. In the early stage of ontology data processing, the goal of the algorithm is to find the location of key components through the learning of some ontology sample points, if the relevant concepts and structure information of each ontology vertex with p-dimensional vectors are expressed. The ontology sparse vector itself contains a certain structure, such as the symmetry between components and the binding relationship between certain components, and the algorithm can also be used to dig out the correlation and decisive components between the components. In this paper, the graph structure is used to express these components and their interrelationships, and the optimal solution is obtained by using spectral graph theory and graph optimization techniques. The essence of the proposed ontology learning algorithm is to find the decisive vertices in the graph

G_{β}

. Finally, two experiments show that the given ontology learning algorithm is effective in similarity calculation and ontology mapping in some specific engineering fields. Full article

(This article belongs to the Special Issue Fuzzy Mathematics Applied to Science, Engineering and Sustainability Issues)

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20 pages, 2021 KiB

Open AccessArticle

Use of a Refined Corporate Social Responsibility Model to Mitigate Information Asymmetry and Evaluate Performance

by Ya-Lan Wang, Kao-Yi Shen, Jim-Yuh Huang and Pin Luarn

Symmetry 2020, 12(8), 1349; https://doi.org/10.3390/sym12081349 - 12 Aug 2020

Cited by 10 | Viewed by 3065

Abstract

While the importance of Corporate Sociable Responsibility (CSR) has been widely acknowledged, research on how to guide a company in evaluating and improving its CSR performance is relatively under-explored. This paper adopts the predominant framework from the United Nations (UN) and proposes a [...] Read more.

While the importance of Corporate Sociable Responsibility (CSR) has been widely acknowledged, research on how to guide a company in evaluating and improving its CSR performance is relatively under-explored. This paper adopts the predominant framework from the United Nations (UN) and proposes a refined CSR model by using a hybrid multiple criteria decision-making (MCDM) approach. The proposed approach is expected to mitigate the potential information asymmetry issue that might deteriorate the CSR performance of a company. To illustrate the hybrid approach, this study analyzes the CSR performance of four publicly listed information technology (IT) manufacturing companies with the participation of senior domain experts, by using the proposed approach. The CSR performance ranking results are consistent by using various experiments, which is similar to the annual CSR contest held by a prominent organization from Taiwan in 2019. In addition, we illustrate how to apply this refined model to gain managerial insights and pursue sustainable CSR improvement with a priority. Full article

(This article belongs to the Special Issue Fuzzy Mathematics Applied to Science, Engineering and Sustainability Issues)

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16 pages, 2985 KiB

Open AccessArticle

Using Fuzzy Sets and Markov Chain Method to Carry out Inventory Strategies with Different Recovery Levels

by Tseng-Fung Ho, Chi-Chung Lin and Chih-Ling Lin

Symmetry 2020, 12(8), 1226; https://doi.org/10.3390/sym12081226 - 26 Jul 2020

Cited by 4 | Viewed by 2145

Abstract

In this study, we first analyze the usability of recycling products, and use the fuzzy set method to determine the main impact on recycling items and their corresponding weights by using the Analytic Hierarchy Process (AHP) to identify various impact recycling levels. The [...] Read more.

In this study, we first analyze the usability of recycling products, and use the fuzzy set method to determine the main impact on recycling items and their corresponding weights by using the Analytic Hierarchy Process (AHP) to identify various impact recycling levels. The Group Decision Supporting System (GDSS) determines the test standards for the recycling rating. It provides a convenient way for recyclers or manufacturers to classify their own products and use fuzzy numbers to select a set of test standards. It can deduce the recovery rate and remanufacturing rate of different recycling processing levels through the Markov chain model to find out the inventory model and total cost. In the numerical analysis, we found that a recycling rate of more than 90% is probably a necessary decision. Since the processing cost of the 100% recovery rate is doubled, the inventory level and total cost will increase with it. Therefore, this study was combined with the reverse logistics method to find the appropriate decision-making strategy and plan, such as the optimal inventory level and recovery rate. Full article

(This article belongs to the Special Issue Fuzzy Mathematics Applied to Science, Engineering and Sustainability Issues)

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25 pages, 774 KiB

Open AccessArticle

A Symmetric Banzhaf Cooperation Value for Games with a Proximity Relation among the Agents

by Inés Gallego, Julio R. Fernández, Andrés Jiménez-Losada and Manuel Ordóñez

Symmetry 2020, 12(7), 1196; https://doi.org/10.3390/sym12071196 - 20 Jul 2020

Cited by 1 | Viewed by 2378

Abstract

A cooperative game represents a situation in which a set of agents form coalitions in order to achieve a common good. To allocate the benefits of the result of this cooperation there exist several values such as the Shapley value or the Banzhaf [...] Read more.

A cooperative game represents a situation in which a set of agents form coalitions in order to achieve a common good. To allocate the benefits of the result of this cooperation there exist several values such as the Shapley value or the Banzhaf value. Sometimes it is considered that not all communications between players are feasible and a graph is introduced to represent them. Myerson (1977) introduced a Shapley-type value for these situations. Another model for cooperative games is the Owen model, Owen (1977), in which players that have similar interests form a priori unions that bargain as a block in order to get a fair payoff. The model of cooperation introduced in this paper combines these two models following Casajus (2007). The situation consists of a communication graph where a two-step value is defined. In the first step a negotiation among the connected components is made and in the second one players inside each connected component bargain. This model can be extended to fuzzy contexts such as proximity relations that consider leveled closeness between agents as we proposed in 2016. There are two extensions of the Banzhaf value to the Owen model, because the natural way loses the group symmetry property. In this paper we construct an appropriate value to extend the symmetric option for situations with a proximity relation and provide it with an axiomatization. Then we apply this value to a political situation. Full article

(This article belongs to the Special Issue Fuzzy Mathematics Applied to Science, Engineering and Sustainability Issues)

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27 pages, 781 KiB

Open AccessArticle

The Linguistic Picture Fuzzy Set and Its Application in Multi-Criteria Decision-Making: An Illustration to the TOPSIS and TODIM Methods Based on Entropy Weight

by Donghai Liu, Yan Luo and Zaiming Liu

Symmetry 2020, 12(7), 1170; https://doi.org/10.3390/sym12071170 - 14 Jul 2020

Cited by 22 | Viewed by 3177

Abstract

The paper considers the multi-criteria decision-making problem based on linguistic picture fuzzy information. Firstly, we propose the concept of linguistic picture fuzzy set(LPFS), where the positive-membership, the neutral-membership and the negative-membership are represented by linguistic variables, and its operation rules are also discussed. [...] Read more.

The paper considers the multi-criteria decision-making problem based on linguistic picture fuzzy information. Firstly, we propose the concept of linguistic picture fuzzy set(LPFS), where the positive-membership, the neutral-membership and the negative-membership are represented by linguistic variables, and its operation rules are also discussed. The linguistic picture fuzzy weighted averaging (LPFWA) operator and linguistic picture fuzzy weighted geometric (LPFWG) operator are developed based on the proposed operation rules. Secondly, we propose the generalized weighted distance measure, the generalized weighted Hausdorff distance measure, and the generalized hybrid weighted distance measure between LPFSs and discuss their properties. Thirdly, we extend the technique for order of preference by similarity to the ideal solution (TOPSIS) method and the TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) method to the proposed distance measure, and the linguistic picture fuzzy entropy method is proposed to calculate the weights of the criteria. Finally, an illustrative example is given to verify the feasibility and effectiveness of the proposed methods, the comparative analysis with other existing methods and sensitivity analysis of the proposed methods are also discussed. Full article

(This article belongs to the Special Issue Fuzzy Mathematics Applied to Science, Engineering and Sustainability Issues)

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21 pages, 1656 KiB

Open AccessArticle

The Linguistic Interval-Valued Intuitionistic Fuzzy Aggregation Operators Based on Extended Hamacher T-Norm and S-Norm and Their Application

by Wei-Bo Zhu, Bin Shuai and Shi-Hang Zhang

Symmetry 2020, 12(4), 668; https://doi.org/10.3390/sym12040668 - 23 Apr 2020

Cited by 15 | Viewed by 2814

Abstract

Linguistic interval-valued intuitionistic fuzzy sets, as an extension of interval-valued intuitionistic fuzzy sets, have strong practical value in the management of complex uncertainty system with qualitative evaluation information. This study focuses on the development of several linguistic interval-valued intuitionistic fuzzy Hamacher (LIVIFH) aggregation [...] Read more.

Linguistic interval-valued intuitionistic fuzzy sets, as an extension of interval-valued intuitionistic fuzzy sets, have strong practical value in the management of complex uncertainty system with qualitative evaluation information. This study focuses on the development of several linguistic interval-valued intuitionistic fuzzy Hamacher (LIVIFH) aggregation operators based on the extended Hamacher t-norm and s-norm. First, the extended Hamacher t-norm and s-norm, which are applicable to linguistic information environment, are applied to define the linguistic interval-valued intuitionistic fuzzy Hamacher operational laws. Second, based on the proposed operational laws, this study defines the linguistic interval-valued intuitionistic fuzzy Hamacher weighted average (LIVIFHWA) operator and the linguistic interval-valued intuitionistic fuzzy Hamacher weighted geometric (LIVIFHWG) operator, and then investigates their properties. Furthermore, the degeneracy and monotonicity of the proposed operators with respect to the adjustable parameter are explored. Finally, a multiple attribute group decision-making (MAGDM) approach is developed based on the proposed LIVIFH aggregation operators, and then this approach is applied to a supplier selection problem. Parameter analysis indicates that the adjustable parameter in the proposed LIVIFH aggregation operators could reflect the attitudes of decision makers. The LIVIFHWA operator would be more appropriate to optimistic decision makers, and the LIVIFHWG operator to pessimistic decision makers. In addition, as the adjustable parameter increasing, both attitudes tend to be neutral. The proposed method is also compared with two other approaches to show its feasibility and efficiency. Full article

(This article belongs to the Special Issue Fuzzy Mathematics Applied to Science, Engineering and Sustainability Issues)

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24 pages, 3443 KiB

Open AccessArticle

Fuzzy-Based Symmetrical Multi-Criteria Decision-Making Procedure for Evaluating the Impact of Harmful Factors of Healthcare Information Security

by Rajeev Kumar, Abhishek Kumar Pandey, Abdullah Baz, Hosam Alhakami, Wajdi Alhakami, Alka Agrawal and Raees Ahmad Khan

Symmetry 2020, 12(4), 664; https://doi.org/10.3390/sym12040664 - 22 Apr 2020

Cited by 42 | Viewed by 4395

Abstract

Growing concern about healthcare information security in the wake of alarmingly rising cyber-attacks is being given symmetrical priority by current researchers and cyber security experts. Intruders are penetrating symmetrical mechanisms of healthcare information security continuously. In the same league, the paper presents an [...] Read more.

Growing concern about healthcare information security in the wake of alarmingly rising cyber-attacks is being given symmetrical priority by current researchers and cyber security experts. Intruders are penetrating symmetrical mechanisms of healthcare information security continuously. In the same league, the paper presents an overview on the current situation of healthcare information and presents a layered model of healthcare information management in organizations. The paper also evaluates the various factors that have a key contribution in healthcare information security breaches through a hybrid fuzzy-based symmetrical methodology of AHP-TOPSIS. Furthermore, for assessing the effect of the calculated results, the authors have tested the results on local hospital software of Varanasi. Tested results of the factors are validated through the comparison and sensitivity analysis in this study. Tabulated results of the proposed study propose a symmetrical mechanism as the most conversant technique which can be employed by the experts and researchers for preparing security guidelines and strategies. Full article

(This article belongs to the Special Issue Fuzzy Mathematics Applied to Science, Engineering and Sustainability Issues)

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20 pages, 5599 KiB

Open AccessArticle

A Monte Carlo Approach to Estimate the Stability of Soil–Rock Slopes Considering the Non-Uniformity of Materials

by Aizhao Zhou, Xianwen Huang, Na Li, Pengming Jiang and Wei Wang

Symmetry 2020, 12(4), 590; https://doi.org/10.3390/sym12040590 - 8 Apr 2020

Cited by 14 | Viewed by 3520

Abstract

A soil–rock slope is a heterogeneous slope composed of soil and rocks that is widely distributed throughout the world. In order to accurately analyze the slope stability of soil–rock mixture, based on a Monte Carlo algorithm (fuzzy-based method), a symmetrical stability analyzing method [...] Read more.

A soil–rock slope is a heterogeneous slope composed of soil and rocks that is widely distributed throughout the world. In order to accurately analyze the slope stability of soil–rock mixture, based on a Monte Carlo algorithm (fuzzy-based method), a symmetrical stability analyzing method for soil–rock slopes is proposed, considering the dispersion of strength of soil–rock mixtures. In analyzing it, the numerical model is symmetrical to the real soil–rock slope in geometry and material properties. In addition, the effect of rock content to slope stability was studied by this symmetrical method. The specific work of this paper is as follows: (1) The acquisition method of random number series for the Monte Carlo algorithm and the method of slope stability analysis, using the Monte Carlo method, are introduced. (2) According to in situ samples and remade samples, the strength characteristics of soil–rock mixtures were measured with different rock contents, which proved the scatter of strength of soil–rock mixtures. (3) Based on the measured strength parameters of soil–rock mixtures and the slope landslide, the reliability in analyzing results and superiority in calculating time of using the Monte Carlo method to analyze stability of soil–rock slopes are detailed. (4) The stability of soil–rock slopes with different rock content is discussed with the Monte Carlo method, and it is concluded that with the increase of rock content, the stability of a soil–rock slope decreases first and then increases, and the minimum safety factor is acquired at 20% rock content. (5) Based on a large number of calculation examples, the applied situations of the Monte Carlo method to analyze stability of soil–rock slopes are detailed according to sampling results and rock size. Full article

(This article belongs to the Special Issue Fuzzy Mathematics Applied to Science, Engineering and Sustainability Issues)

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26 pages, 3360 KiB

Open AccessArticle

Fuzzy Model for Risk Assessment of Machinery Failures

by Dejan V. Petrović, Miloš Tanasijević, Saša Stojadinović, Jelena Ivaz and Pavle Stojković

Symmetry 2020, 12(4), 525; https://doi.org/10.3390/sym12040525 - 3 Apr 2020

Cited by 20 | Viewed by 4200

Abstract

The main goal of this research was the development of an algorithm for the implementation of negative risk parameters in a synthesis model for a risk level assessment for a specific machine used in the mining industry. Fuzzy sets and fuzzy logic theory, [...] Read more.

The main goal of this research was the development of an algorithm for the implementation of negative risk parameters in a synthesis model for a risk level assessment for a specific machine used in the mining industry. Fuzzy sets and fuzzy logic theory, in combination with statistical methods, were applied to analyze the time picture state of the observed machine. Fuzzy logic is presented through fuzzy proposition and a fuzzy composition module. Using these tools, the symmetric position of the fuzzy sets with regard to class was used, and the symmetric fuzzy inference approach was used in an outcome calculation. The main benefit of the proposed model is being able to use numerical and linguistic data in a risk assessment model. The proposed risk assessment model, using fuzzy logic conclusions and min–max composition, was used on a mobile crushing machine. The results indicated that the risk level of the mobile crushing machine was in the “high” category, which means that it is necessary to introduce maintenance policies based on this high risk. The proposed risk assessment model is useful for any engineering system. Full article

(This article belongs to the Special Issue Fuzzy Mathematics Applied to Science, Engineering and Sustainability Issues)

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12 pages, 222 KiB

Open AccessArticle

An EDAS Method for Multiple Attribute Group Decision-Making under Intuitionistic Fuzzy Environment and Its Application for Evaluating Green Building Energy-Saving Design Projects

by Yuan Liang

Symmetry 2020, 12(3), 484; https://doi.org/10.3390/sym12030484 - 23 Mar 2020

Cited by 55 | Viewed by 4144

Abstract

Multiple attribute group decision-making (MAGDM) methods have a significant influence on decision-making in a variety of strategic fields, including science, business and real-life studies. The problem of evaluation in green building energy-saving design projects could be regarded as a type of MAGDM problem. [...] Read more.

Multiple attribute group decision-making (MAGDM) methods have a significant influence on decision-making in a variety of strategic fields, including science, business and real-life studies. The problem of evaluation in green building energy-saving design projects could be regarded as a type of MAGDM problem. The evaluation based on distance from average solution (EDAS) method is one of the MAGDM methods, which simplifies the traditional decision-making process. Symmetry among some attributes that are known and unknown as well as between pure attribute sets and fuzzy attribute membership sets can be an effective way to solve MAGDM problems. In this paper, the classical EDAS method is extended to intuitionistic fuzzy environments to solve some MAGDM issues. First, some concepts of intuitionistic fuzzy sets (IFSs) are briefly reviewed. Then, by integrating the EDAS method with IFSs, we establish an IF-EDAS method to solve the MAGDM issues and present all calculating procedures in detail. Finally, we provide an empirical application for evaluating green building energy-saving design projects to demonstrate this novel method. Some comparative analyses are also made to show the merits of the method. Full article

(This article belongs to the Special Issue Fuzzy Mathematics Applied to Science, Engineering and Sustainability Issues)

22 pages, 356 KiB

Open AccessFeature PaperArticle

On Two Classes of Soft Sets in Soft Topological Spaces

by Samer Al Ghour and Worood Hamed

Symmetry 2020, 12(2), 265; https://doi.org/10.3390/sym12020265 - 9 Feb 2020

Cited by 62 | Viewed by 3554

Abstract

In this paper, we define soft

ω

-open sets and strongly soft

ω

-open sets as two new classes of soft sets. We study the natural properties of these types of soft sets and we study the validity of the exact versions of [...] Read more.

In this paper, we define soft

ω

-open sets and strongly soft

ω

-open sets as two new classes of soft sets. We study the natural properties of these types of soft sets and we study the validity of the exact versions of some known results in ordinary topological spaces regarding

ω

-open sets in soft topological spaces. Also, we study the relationships between the

ω

-open sets of a given indexed family of topological spaces and the soft

ω

-open sets (resp. strongly soft

ω

-open sets) of their generated soft topological space. These relationships form a biconditional logical connective which is a symmetry. As an application of strongly soft

ω

-open sets, we characterize soft Lindelof (resp. soft weakly Lindelof) soft topological spaces. Full article

(This article belongs to the Special Issue Fuzzy Mathematics Applied to Science, Engineering and Sustainability Issues)

11 pages, 362 KiB

Open AccessArticle

Fuzzy Information Retrieval Based on Continuous Bag-of-Words Model

by Dong Qiu, Haihuan Jiang and Shuqiao Chen

Symmetry 2020, 12(2), 225; https://doi.org/10.3390/sym12020225 - 3 Feb 2020

Cited by 17 | Viewed by 5715

Abstract

In this paper, we study the feasibility of performing fuzzy information retrieval by word embedding. We propose a fuzzy information retrieval approach to capture the relationships between words and query language, which combines some techniques of deep learning and fuzzy set theory. We [...] Read more.

In this paper, we study the feasibility of performing fuzzy information retrieval by word embedding. We propose a fuzzy information retrieval approach to capture the relationships between words and query language, which combines some techniques of deep learning and fuzzy set theory. We try to leverage large scale data and the continuous-bag-of words model to find the relevant feature of words and obtain word embedding. To enhance retrieval effectiveness, we measure the relativity among words by word embedding, with the property of symmetry. Experimental results show that the recall ratio, precision ratio, and harmonic average of two ratios of the proposed method outperforms the ones of the traditional methods. Full article

(This article belongs to the Special Issue Fuzzy Mathematics Applied to Science, Engineering and Sustainability Issues)

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18 pages, 2548 KiB

Open AccessArticle

Design and Control of a Wall Cleaning Robot with Adhesion-Awareness

by M. A. Viraj J. Muthugala, Manuel Vega-Heredia, Rajesh Elara Mohan and Suresh Raj Vishaal

Symmetry 2020, 12(1), 122; https://doi.org/10.3390/sym12010122 - 8 Jan 2020

Cited by 51 | Viewed by 7746

Abstract

Wall cleaning robots are developed to cater to the demands of the building maintenance sector. The ability to climb vertical surfaces is one of the crucial requirements of a wall cleaning robot. Robots that can climb vertical surfaces by adhesion to a surface [...] Read more.

Wall cleaning robots are developed to cater to the demands of the building maintenance sector. The ability to climb vertical surfaces is one of the crucial requirements of a wall cleaning robot. Robots that can climb vertical surfaces by adhesion to a surface are preferred since those do not require additional support structures. Vacuum suction mechanisms are widely used in this regard. The suction force acting on the robot due to the negative pressure built up is used by these robots for the adhesion. A robot will fall off or overturn when the pressure difference drops down a certain threshold. In contrast, if the pressure difference becomes too high, the excessive amount of frictional forces will hinder the locomotion ability. Moreover, a wall cleaning robot should be capable of adapting the adhesion force to maintain the symmetry between safe adhesion and reliable locomotion since adhesion forces which are too low or too high hinder the safety of adhesion and reliability of locomotion respectively. Thus, the pressure difference needs to be sustained within a desired range to ensure a robot’s safety and reliability. However, the pressure difference built up by a vacuum system may unpredictably vary due to unexpected variation of air leakages due to irregularities in surfaces. The existing wall cleaning robots that use vacuum suction mechanisms for adhesion are not aware of the adhesion status, or subsequently responding to them. Therefore, this paper proposes a design for a wall cleaning robot that is capable of adapting vacuum power based on the adhesion-awareness to improve safety and reliability. A fuzzy inference system is proposed here to adapt the vacuum power based on the variation of the adhesion and the present power setting of the vacuum. Moreover, an application of fuzzy logic to produce a novel controlling criterion for a wall cleaning robot to ensure safety and reliability of operation is proposed. A fuzzy inference system was used to achieve the control goals, since the exact underlying dynamics of the vacuum-adhesion cannot be mathematically modeled. The design details of the robot are presented with due attention to the proposed control strategy. Experimental results confirmed that the performance of a robot with proposed adhesion-awareness surpasses that of a robot with no adhesion-awareness in the aspects of safety, reliability, and efficiency. The limitations of the work and future design suggestions are also discussed. Full article

(This article belongs to the Special Issue Fuzzy Mathematics Applied to Science, Engineering and Sustainability Issues)

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9 pages, 241 KiB

Open AccessArticle

Fuzzy Logic Applied to Sustainable Development Goals and Human Trafficking

by John N Mordeson and Sunil Mathew

Symmetry 2020, 12(1), 87; https://doi.org/10.3390/sym12010087 - 2 Jan 2020

Cited by 5 | Viewed by 2581

Abstract

In 2015, the leaders of all the UN’s Member States agreed to the 2030 Agenda for Sustainable Development. The 17 Sustainable Development Goals and their 169 associated targets address five areas of critical importance: people, planet, prosperity, peace, and partnership. The purpose of [...] Read more.

In 2015, the leaders of all the UN’s Member States agreed to the 2030 Agenda for Sustainable Development. The 17 Sustainable Development Goals and their 169 associated targets address five areas of critical importance: people, planet, prosperity, peace, and partnership. The purpose of this paper is to take the metrics and data provided and transform them into a fuzzy logic setting. This allows for the analysis of the results in SDG Index and Dashboards Report 2019 by using the techniques of fuzzy logic. Many of these 17 Sustainable Development Goals are related to the terrible crime of human trafficking. We also examine these goals in a fuzzy logic setting. Full article

(This article belongs to the Special Issue Fuzzy Mathematics Applied to Science, Engineering and Sustainability Issues)

13 pages, 1456 KiB

Open AccessArticle

Type 2 Fuzzy Inference-Based Time Series Model

by Nur Fazliana Rahim, Mahmod Othman, Rajalingam Sokkalingam and Evizal Abdul Kadir

Symmetry 2019, 11(11), 1340; https://doi.org/10.3390/sym11111340 - 31 Oct 2019

Cited by 4 | Viewed by 2638

Abstract

Fuzzy techniques have been suggested as useful method for forecasting performance. However, its dependency on experts’ knowledge causes difficulties in information extraction and data collection. Therefore, to overcome the difficulties, this research proposed a new type 2 fuzzy time series (T₂FTS) [...] Read more.

Fuzzy techniques have been suggested as useful method for forecasting performance. However, its dependency on experts’ knowledge causes difficulties in information extraction and data collection. Therefore, to overcome the difficulties, this research proposed a new type 2 fuzzy time series (T₂FTS) forecasting model. The T₂FTS model was used to exploit more information in time series forecasting. The concepts of sliding window method (SWM) and fuzzy rule-based systems (FRBS) were incorporated in the utilization of T₂FTS to obtain forecasting values. A sliding window method was proposed to find a proper and systematic measurement for predicting the number of class intervals. Furthermore, the weighted subsethood-based algorithm was applied in developing fuzzy IF–THEN rules, where it was later used to perform forecasting. This approach provides inferences based on how people think and make judgments. In this research, the data sets from previous studies of crude palm oil prices were used to further analyze and validate the proposed model. With suitable class intervals and fuzzy rules generated, the forecasting values obtained were more precise and closer to the actual values. The findings of this paper proved that the proposed forecasting method could be used as an alternative for improved forecasting of sustainable crude palm oil prices. Full article

(This article belongs to the Special Issue Fuzzy Mathematics Applied to Science, Engineering and Sustainability Issues)

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21 pages, 1138 KiB

Open AccessArticle

Group Decision-Making Based on the VIKOR Method with Trapezoidal Bipolar Fuzzy Information

by Shumaiza, Muhammad Akram, Ahmad N. Al-Kenani and José Carlos R. Alcantud

Symmetry 2019, 11(10), 1313; https://doi.org/10.3390/sym11101313 - 19 Oct 2019

Cited by 86 | Viewed by 7498

Abstract

The VIKOR methodology stands out as an important multi-criteria decision-making technique. VIKOR stands for “VIekriterijumsko KOmpromisno Rangiranje”, a Serbian term for “multi-criteria optimization and compromise solution”. It has been adapted to sources of information with sundry formats. We contribute to that strand on [...] Read more.

The VIKOR methodology stands out as an important multi-criteria decision-making technique. VIKOR stands for “VIekriterijumsko KOmpromisno Rangiranje”, a Serbian term for “multi-criteria optimization and compromise solution”. It has been adapted to sources of information with sundry formats. We contribute to that strand on literature with a design of a new multiple-attribute group decision-making method called the trapezoidal bipolar fuzzy VIKOR method. It consists of a suitable redesign of the VIKOR approach so that it can use information with bipolar configurations. Bipolar fuzzy sets (and numbers) establish a symmetrical trade-off between two judgmental constituents of human thinking. The agents acquire uncertain and vague information in the form of linguistic variables parameterized by trapezoidal bipolar fuzzy numbers. Trapezoidal bipolar fuzzy numbers are considered by decision-makers for assigning the preference information of alternatives with respect to different attributes. Our non-trivial adaptation necessitates several steps. The ranking function of bipolar fuzzy numbers is employed to make a simple decision matrix with real numbers as its entries. Shannon’s entropy concept is applied to evaluate the normalized weights for attributes that may be either partially or completely unknown to the decision-makers. The ordering of the alternatives is obtained by assorting the maximum group utility and the individual regret of the opponent in an ascending manner. For illustration, the proposed technique is applied to two group decision-making problems, namely, the selection of waste treatment methods and the site to plant a thermal power station. A comparison of this method with the trapezoidal bipolar fuzzy TOPSIS method is also presented. Full article

(This article belongs to the Special Issue Fuzzy Mathematics Applied to Science, Engineering and Sustainability Issues)

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10 pages, 241 KiB

Open AccessArticle

Solving Triangular Intuitionistic Fuzzy Matrix Game by Applying the Accuracy Function Method

by Yumei Xing and Dong Qiu

Symmetry 2019, 11(10), 1258; https://doi.org/10.3390/sym11101258 - 9 Oct 2019

Cited by 15 | Viewed by 2386

Abstract

In this paper, the matrix game based on triangular intuitionistic fuzzy payoff is put forward. Then, we get a conclusion that the equilibrium solution of this game model is equivalent to the solution of a pair of the primal–dual single objective intuitionistic fuzzy [...] Read more.

In this paper, the matrix game based on triangular intuitionistic fuzzy payoff is put forward. Then, we get a conclusion that the equilibrium solution of this game model is equivalent to the solution of a pair of the primal–dual single objective intuitionistic fuzzy linear optimization problems

(I F L O P 1)

and

(I F L O D 1)

. Furthermore, by applying the accuracy function, which is linear, we transform the primal–dual single objective intuitionistic fuzzy linear optimization problems

(I F L O P 1)

and

(I F L O D 1)

into the primal–dual discrete linear optimization problems

(G L O P 1)

and

(G L O D 1) .

The above primal–dual pair

(G L O P 1)

–

(G L O D 1)

is symmetric in the sense the dual of

(G L O D 1)

is

(G L O P 1)

. Thus the primal–dual discrete linear optimization problems

(G L O P 1)

and

(G L O D 1)

are called the symmetric primal–dual discrete linear optimization problems. Finally, the technique is illustrated by an example. Full article

(This article belongs to the Special Issue Fuzzy Mathematics Applied to Science, Engineering and Sustainability Issues)

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