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New Trends in Fuzzy Sets Theory and Their Extensions
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New Trends in Fuzzy Sets Theory and Their Extensions

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Fuzzy Sets, Systems and Decision Making".

Deadline for manuscript submissions: closed (31 May 2022) | Viewed by 28988

Special Issue Editors

Dr. Zhen-Song Chen

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Guest Editor
Department of Engineering Management, School of Civil Engineering, Wuhan University, Wuhan 430072, China
Interests: engineering management; decision support; computational semantics analysis; group decision making; computing with words
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Witold Pedrycz

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Guest Editor
Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6G 2E1, Canada
Interests: fuzzy set theory; pattern clustering; learning (artificial intelligence); decision making; granular
Special Issues, Collections and Topics in MDPI journals
Dr. Lesheng Jin

E-Mail Website
Guest Editor
Business School, Nanjing Normal University, Nanjing, China
Interests: preference involved decision making; linguistic decision making; information fusion; aggregation operators
Special Issues, Collections and Topics in MDPI journals
Dr. Rosa M. Rodriguez

grade E-Mail Website
Guest Editor
Department of Computer Science, University of Jaén, 23071 Jaén, Spain
Interests: linguistic preference modelling; fuzzy decision making; decision support system; computing with words
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Luis Martínez López

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Guest Editor
Department of Computer Science, University of Jaén, 23071 Jaén, Spain
Interests: computational intelligence; fuzzy decision making; recommender systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues, 

Fuzzy sets theory, since its inception in 1965, has received wide attention from academia and practitioners and has achieved significant advancements in various scientific frontiers. As a novel conceptual framework to facilitate the characterization of human-centric systems, fuzzy sets theory has been proven to be an efficient and powerful tool in modelling human centricity featured in intelligent systems that accomplish advancements of computational intelligence in many domains, such as data mining, data analytics, image understanding and interpretation, recommender systems, explainable artificial intelligence (XAI), etc.

Computing with fuzzy sets has been the central task when it comes to the theoretical development of fuzzy sets theory, and granular computing has offered processing principles that open new frontiers to deal with it as being well elaborated in Prof. Witold Pedrycz’s recently published monograph entitled “An Introduction to Computing with Fuzzy Sets: Analysis, Design, and Applications”. The goal of this Special Issue is to further explore the new trends of fuzzy sets theory in emerging research fields of computational intelligence and the new frontiers that promote a broad and up-to-date understanding of fuzzy-sets-theory-based extensions and applications. The entire academic community has witnessed the gradual paradigm shift of fuzzy sets theory in both its theoretical and methodological aspects, as well as its applications in a variety of disciplines of science and engineering.

The Special Issue welcomes original contributions that advance the state-of-the-art fuzzy-sets-theory-based concepts, methodologies, algorithms and applications in several emerging and related topics. Special attention of this Special Issue will be paid to the following research topics: a) new fuzzy representation models, b) fuzzy machine learning, c) granular fuzzy models, d) data-driven fuzzy modeling, e) fuzzy information fusion and aggregation functions, f) fuzzy logic, and g) fuzzy set theory-based applications in science and engineering.

Dr. Zhen-Song Chen
Prof. Dr. Witold Pedrycz
Dr. Lesheng Jin
Dr. Rosa M. Rodriguez
Prof. Dr. Luis Martínez López
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fuzzy rules and reasoning
  • fuzzy set operations
  • fuzzy measures
  • fuzzy logic
  • fuzzy relations and relational computing
  • information granules and granular computing
  • fuzzy-based linguistic approximation
  • fuzzy set transformation and fuzzy arithmetic
  • higher type, higher order fuzzy sets and hybrid fuzzy sets
  • fuzzy partitions
  • fuzzy information fusion
  • fuzzy neurocomputing
  • granular fuzzy models
  • explainable artificial intelligence (XAI)
  • fuzzy-based data mining
  • elicitation of membership functions
  • fuzzy decision theory
  • fuzzy control systems
  • fuzzy decision making
  • fuzzy-sets-theory-based applications

Published Papers (16 papers)

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Research

20 pages, 2206 KiB  
Article
A Novel Early Warning Method for Handling Non-Homogeneous Information
by Zi-Xin Zhang, Liang Wang and Ying-Ming Wang
Mathematics 2022, 10(16), 3016; https://doi.org/10.3390/math10163016 - 21 Aug 2022
Cited by 4 | Viewed by 1176
Abstract
Early warnings are an indispensable part of emergency management, which is a powerful way to eliminate or reduce the negative impacts caused by emergencies in advance. Early warning problems have been discussed from different perspectives and have obtained fruitful results. Information plays a [...] Read more.
Early warnings are an indispensable part of emergency management, which is a powerful way to eliminate or reduce the negative impacts caused by emergencies in advance. Early warning problems have been discussed from different perspectives and have obtained fruitful results. Information plays a critical role in all kinds of decision problems, with no exception for the early warning problem. There are various information types related to emergencies in real-world situations; however, existing early warning studies only considered a single information type, which might not describe the problem properly and comprehensively. To enrich existing early warning studies, a novel early warning method considering non-homogeneous information together with experts’ hesitation is proposed, in which numerical values, interval values, linguistic terms, and hesitant fuzzy linguistic terms are considered. To facilitate the computations with non-homogeneous information, a transformation process needs to be conducted. On such a basis, a fuzzy TOPSIS method based on alpha-level sets is employed to handle the transformed fuzzy information due to its superiority in obtaining information and its capacity to contain as much information as possible during the early warning process. Additionally, two different options are provided to analyze the status and tendency of early warning objects. Finally, an illustrative example about early warnings about landslides and a related comparison are conducted to demonstrate the novelty, superiority, and feasibility and validity of the proposed method. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Sets Theory and Their Extensions)
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27 pages, 2220 KiB  
Article
Interval Type-2 Fuzzy Envelope of Proportional Hesitant Fuzzy Linguistic Term Set: Application to Large-Scale Group Decision Making
by Yaya Liu, Rosa M. Rodríguez and Luis Martínez
Mathematics 2022, 10(14), 2368; https://doi.org/10.3390/math10142368 - 06 Jul 2022
Cited by 4 | Viewed by 1048
Abstract
Large-scale group decision-making (LS-GDM) problems are common in the daily life of human beings. Both information fusion and computing with words (CWW) technologies in LS-GDM suffer from challenges. In the current research, a proportional hesitant fuzzy linguistic term set (PHFLTS) will be applied [...] Read more.
Large-scale group decision-making (LS-GDM) problems are common in the daily life of human beings. Both information fusion and computing with words (CWW) technologies in LS-GDM suffer from challenges. In the current research, a proportional hesitant fuzzy linguistic term set (PHFLTS) will be applied to capture the preferences of sub-groups in LS-GDM, which decreases the information lost in information fusion processes. Novel fuzzy semantic representation models of PHFLTS, such as type-1 fuzzy envelope and interval type-2 fuzzy envelope, are respectively studied. The application of the proposed fuzzy entropies facilitates the CWW process with the PHFLTS under the framework of a fuzzy linguistic approach. In particular, linguistic uncertainties contained in the PHFLTS can be reflected in a comprehensive way when the type-2 fuzzy envelope is applied, which contributes to the decrease in the information lost during the CWW process. A novel LS-GDM method cooperating with the fuzzy semantic models of PHFLTS is proposed, in which weights for the sub-groups are determined by size, cohesion, and degree of reliability among the sub-groups. Finally, the proposed decision method as well as CWW tools are applied to the process of urban renewal plan selection. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Sets Theory and Their Extensions)
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15 pages, 298 KiB  
Article
Efficient Algorithms for Data Processing under Type-3 (and Higher) Fuzzy Uncertainty
by Vladik Kreinovich, Olga Kosheleva, Patricia Melin and Oscar Castillo
Mathematics 2022, 10(13), 2361; https://doi.org/10.3390/math10132361 - 05 Jul 2022
Cited by 3 | Viewed by 1181
Abstract
It is known that, to more adequately describe expert knowledge, it is necessary to go from the traditional (type-1) fuzzy techniques to higher-order ones: type-2, probably type-3 and even higher. Until recently, only type-1 and type-2 fuzzy sets were used in practical applications. [...] Read more.
It is known that, to more adequately describe expert knowledge, it is necessary to go from the traditional (type-1) fuzzy techniques to higher-order ones: type-2, probably type-3 and even higher. Until recently, only type-1 and type-2 fuzzy sets were used in practical applications. However, lately, it turned out that type-3 fuzzy sets are also useful in some applications. Because of this practical importance, it is necessary to design efficient algorithms for data processing under such type-3 (and higher-order) fuzzy uncertainty. In this paper, we show how we can combine known efficient algorithms for processing type-1 and type-2 uncertainty to come up with a new algorithm for the type-3 case. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Sets Theory and Their Extensions)
14 pages, 312 KiB  
Article
Soft Sets with Atoms
by Andrei Alexandru and Gabriel Ciobanu
Mathematics 2022, 10(12), 1956; https://doi.org/10.3390/math10121956 - 07 Jun 2022
Viewed by 1239
Abstract
The theory of finitely supported structures is used for dealing with very large sets having a certain degree of symmetry. This framework generalizes the classical set theory of Zermelo-Fraenkel by allowing infinitely many basic elements with no internal structure (atoms) and by equipping [...] Read more.
The theory of finitely supported structures is used for dealing with very large sets having a certain degree of symmetry. This framework generalizes the classical set theory of Zermelo-Fraenkel by allowing infinitely many basic elements with no internal structure (atoms) and by equipping classical sets with group actions of the permutation group over these basic elements. On the other hand, soft sets represent a generalization of the fuzzy sets to deal with uncertainty in a parametric manner. In this paper, we study the soft sets in the new framework of finitely supported structures, associating to any crisp set a family of atoms describing it. We prove some finiteness properties for infinite soft sets, some order properties and Tarski-like fixed point results for mappings between soft sets with atoms. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Sets Theory and Their Extensions)
17 pages, 3446 KiB  
Article
Evaluation Method of Highway Plant Slope Based on Rough Set Theory and Analytic Hierarchy Process: A Case Study in Taihang Mountain, Hebei, China
by Luliang Liu, Yuanming Dou and Jiangang Qiao
Mathematics 2022, 10(8), 1264; https://doi.org/10.3390/math10081264 - 11 Apr 2022
Cited by 5 | Viewed by 1402
Abstract
The material foundation of soil and water conservation is built on the integrity of the highway plant slope. The proportional relevance of the components that affect slope quality was evaluated based on an environmental assessment and the actual characteristics of the highway slope. [...] Read more.
The material foundation of soil and water conservation is built on the integrity of the highway plant slope. The proportional relevance of the components that affect slope quality was evaluated based on an environmental assessment and the actual characteristics of the highway slope. A system of four major indexes and twelve secondary indexes comprising plant traits, geometric factors, hydrological conditions, and vegetation conditions was developed to assess the stability of roadway plant slopes. The rough set theory approach and the analytic hierarchy process were used to solve the weights of the slope evaluation indexes. Based on a rough set and an analytic hierarchy process, an evaluation model is proposed. The model eliminates the inconsistency and uncertainty in the evaluated factors that are used to calculate the slope. The study was conducted in China. The highway plant slope of the Taihang Mountain highway in the Hebei province was evaluated using the assessment model after dividing the highway plant slope stability into four grades. According to the evaluation results, the model can be used as a reference highway plant slope stability study and provide technical help to prevent and lower slope safety accidents. The evaluation model can predict the slope quality of highway plants, demonstrating the efficacy and reliability of the evaluation methodology and approach. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Sets Theory and Their Extensions)
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16 pages, 330 KiB  
Article
An Efficient Approach to Approximate Fuzzy Ideals of Semirings Using Bipolar Techniques
by Muhammad Shabir, Ahmad N. Al-Kenani, Fawad Javed and Shahida Bashir
Mathematics 2022, 10(7), 1009; https://doi.org/10.3390/math10071009 - 22 Mar 2022
Cited by 6 | Viewed by 1444
Abstract
The bipolar fuzzy (BF) set is an extension of the fuzzy set used to solve the uncertainty of having two poles, positive and negative. The rough set is a useful mathematical technique to handle vagueness and impreciseness. The major objective of this paper [...] Read more.
The bipolar fuzzy (BF) set is an extension of the fuzzy set used to solve the uncertainty of having two poles, positive and negative. The rough set is a useful mathematical technique to handle vagueness and impreciseness. The major objective of this paper is to analyze the notion of approximation of BF ideals of semirings by combining the theories of the rough and BF sets. Then, the idea of rough approximation of BF subsemirings (ideals, bi-ideals and interior ideals) of semirings is developed. In addition, semirings are characterized by upper and lower rough approximations using BF ideals. Further, it is seen that congruence relations (CRs) and complete congruence relations (CCRs) play fundamental roles for rough approximations of bipolar fuzzy ideals. Therefore, their associated properties are investigated by means of CRs and CCRs. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Sets Theory and Their Extensions)
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33 pages, 650 KiB  
Article
T-Spherical Fuzzy Bonferroni Mean Operators and Their Application in Multiple Attribute Decision Making
by Wei Yang and Yongfeng Pang
Mathematics 2022, 10(6), 988; https://doi.org/10.3390/math10060988 - 19 Mar 2022
Cited by 25 | Viewed by 1999
Abstract
To deal with complicated decision problems with T-Spherical fuzzy values in the aggregation process, T-Spherical fuzzy Bonferroni mean operators are developed by extending the Bonferroni mean and Dombi mean to a T-Spherical fuzzy environment. The T-spherical fuzzy interaction Bonferroni mean operator and the [...] Read more.
To deal with complicated decision problems with T-Spherical fuzzy values in the aggregation process, T-Spherical fuzzy Bonferroni mean operators are developed by extending the Bonferroni mean and Dombi mean to a T-Spherical fuzzy environment. The T-spherical fuzzy interaction Bonferroni mean operator and the T-spherical fuzzy interaction geometric Bonferroni mean operator are first defined. Then, the T-spherical fuzzy interaction weighted Bonferroni mean operator and the T-spherical fuzzy weighted interaction geometric Bonferroni mean operator are defined. Based on the Dombi mean and the Bonferroni mean operator, some T-Spherical fuzzy Dombi Bonferroni mean operators are proposed, including the T-spherical fuzzy Dombi Bonferroni mean operator, T-spherical fuzzy geometric Dombi Bonferroni mean operator, T-spherical fuzzy weighted Dombi Bonferroni mean operator and the T-spherical fuzzy weighted geometric Dombi Bonferroni mean operator. The properties of these proposed operators are studied. An attribute weight determining method based on the T-spherical fuzzy entropy and symmetric T-spherical fuzzy cross-entropy is developed. A new decision making method based on the proposed T-Spherical fuzzy Bonferroni mean operators is proposed for partly known or completely unknown attribute weight situations. The furniture procurement problem is presented to illustrate the new algorithm, and some comparisons are made. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Sets Theory and Their Extensions)
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23 pages, 383 KiB  
Article
Pessimistic Multigranulation Rough Set of Intuitionistic Fuzzy Sets Based on Soft Relations
by Muhammad Zishan Anwar, Ahmad N. Al-Kenani, Shahida Bashir and Muhammad Shabir
Mathematics 2022, 10(5), 685; https://doi.org/10.3390/math10050685 - 22 Feb 2022
Cited by 8 | Viewed by 1279
Abstract
Qian presented multigranulation rough set (MGRS) models based on Pawlak’s rough set (RS) model. There are two types of MGRS models, named optimistic MGRS and pessimistic MGRS. Recently, Shabir et al. presented an optimistic multigranulation intuitionistic fuzzy rough set (OMGIFRS) based on soft [...] Read more.
Qian presented multigranulation rough set (MGRS) models based on Pawlak’s rough set (RS) model. There are two types of MGRS models, named optimistic MGRS and pessimistic MGRS. Recently, Shabir et al. presented an optimistic multigranulation intuitionistic fuzzy rough set (OMGIFRS) based on soft binary relations. This paper explores the pessimistic multigranulation intuitionistic fuzzy rough set (PMGIFRS) based on soft relations combined with a soft set (SS) over two universes. The resulting two sets are lower approximations and upper approximations with respect to the aftersets and foresets. Some basic properties of this established model are studied. Similarly, the MGRS of an IFS based on multiple soft relations is presented and some algebraic properties are discussed. Finally, an example is presented that illustrates the importance of the proposed decision-making algorithm. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Sets Theory and Their Extensions)
11 pages, 298 KiB  
Article
Weight Vector Generation in Multi-Criteria Decision-Making with Basic Uncertain Information
by Ya-Qiang Xu, Le-Sheng Jin, Zhen-Song Chen, Ronald R. Yager, Jana Špirková, Martin Kalina and Surajit Borkotokey
Mathematics 2022, 10(4), 572; https://doi.org/10.3390/math10040572 - 12 Feb 2022
Cited by 12 | Viewed by 1643
Abstract
This paper elaborates the different methods to generate normalized weight vector in multi-criteria decision-making where the given information of both criteria and inputs are uncertain and can be expressed by basic uncertain information. Some general weight allocation paradigms are proposed in view of [...] Read more.
This paper elaborates the different methods to generate normalized weight vector in multi-criteria decision-making where the given information of both criteria and inputs are uncertain and can be expressed by basic uncertain information. Some general weight allocation paradigms are proposed in view of their convenience in expression. In multi-criteria decision-making, the given importance for each considered criterion may have different extents of uncertainty. Accordingly, we propose some special induced weight-allocation methods. The inputs can be also associated with varying uncertainty extents, and then we develop several induced weight-generation methods for consideration. In addition, we present some suggested and prescriptive weight allocation rules and analyze their reasonability. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Sets Theory and Their Extensions)
17 pages, 317 KiB  
Article
Water Carrying Capacity Evaluation Method Based on Cloud Model Theory and an Evidential Reasoning Approach
by Wenzhi Cao, Jilin Deng, Yi Yang, Yangyan Zeng and Limei Liu
Mathematics 2022, 10(2), 266; https://doi.org/10.3390/math10020266 - 16 Jan 2022
Cited by 11 | Viewed by 2561
Abstract
The scientific and reasonable evaluation of the carrying capacity of water resources is of guiding significance for solving the issues of water resource shortages and pollution control. It is also an important method for realizing the sustainable development of water resources. Aiming at [...] Read more.
The scientific and reasonable evaluation of the carrying capacity of water resources is of guiding significance for solving the issues of water resource shortages and pollution control. It is also an important method for realizing the sustainable development of water resources. Aiming at an evaluation of the carrying capacity of water resources, an evaluation model based on the cloud model theory and evidential reasoning approach is studied. First, based on the existing indicators, a water resources evaluation index system based on the pressure-state-response (PSR) model is constructed, and a classification method of carrying capacity grade is designed. The cloud model theory is used to realize the transformation between the measured value of indicators and the degree of correlation. Second, to obtain the weight of the evaluation index, the weight method of the index weights model based on the entropy weight method and evidential reasoning approach is proposed. Then, the reliability distribution function of the evaluation index and the graded probability distribution of the carrying capacity of water resources are obtained by an evidential reasoning approach. Finally, the evaluation method of the carrying capacity of water resources is constructed, and specific steps are provided. The proposed method is applied to the evaluation of water resources carrying capacity for Hunan Province, which verifies the feasibility and effectiveness of the method proposed in the present study. This paper applies this method of the evaluation of the water resources carrying capacity of Hunan Province from 2010 to 2019. It is concluded that the water resources carrying capacity of Hunan Province belongs to III~V, which is between the critical state and the strong carrying capacity state. The carrying capacity of the province’s water resources is basically on the rise. This shows that the carrying capacity of water resources in Hunan Province is in good condition, and corresponding protective measures should be taken to continue the current state. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Sets Theory and Their Extensions)
14 pages, 281 KiB  
Article
Solving an Integral Equation via Fuzzy Triple Controlled Bipolar Metric Spaces
by Gunaseelan Mani, Arul Joseph Gnanaprakasam, Zoran D. Mitrović and Monica-Felicia Bota
Mathematics 2021, 9(24), 3181; https://doi.org/10.3390/math9243181 - 09 Dec 2021
Cited by 6 | Viewed by 1795
Abstract
In this paper, motivated by the recent result of Sezen, we introduce the notion of fuzzy triple controlled bipolar metric space and prove some fixed point results in this framework. Our results generalize and extend some of the well-known results from the literature. [...] Read more.
In this paper, motivated by the recent result of Sezen, we introduce the notion of fuzzy triple controlled bipolar metric space and prove some fixed point results in this framework. Our results generalize and extend some of the well-known results from the literature. We also explore some of the applications of our key results to integral equations. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Sets Theory and Their Extensions)
24 pages, 345 KiB  
Article
Semiring-Valued Fuzzy Sets and F-Transform
by Jiří Močkoř
Mathematics 2021, 9(23), 3107; https://doi.org/10.3390/math9233107 - 02 Dec 2021
Cited by 8 | Viewed by 1319
Abstract
The notion of a semiring-valued fuzzy set is introduced for special commutative partially pre-ordered semirings, including basic operations with these fuzzy structures. It is showed that many standard MV-algebra-valued fuzzy type structures with standard operations, such as hesitant, intuitionistic, neutrosophic or [...] Read more.
The notion of a semiring-valued fuzzy set is introduced for special commutative partially pre-ordered semirings, including basic operations with these fuzzy structures. It is showed that many standard MV-algebra-valued fuzzy type structures with standard operations, such as hesitant, intuitionistic, neutrosophic or fuzzy soft sets are, for appropriate semirings, isomorphic to semiring-valued fuzzy sets with operations defined. F-transform and inverse F-transform are introduced for semiring-valued fuzzy sets and properties of these transformations are investigated. Using the transformation of MV-algebra-valued fuzzy type structures to semiring-valued fuzzy sets, the F-transforms for these fuzzy type structures is introduced. The advantage of this procedure is, among other things, that the properties of this F-transform are analogous to the properties of the classical F-transform and because these properties are proven for any semiring-valued fuzzy sets, it is not necessary to prove them for individual fuzzy type structures. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Sets Theory and Their Extensions)
13 pages, 268 KiB  
Article
Measuring Product Similarity with Hesitant Fuzzy Set for Recommendation
by Chunsheng Cui, Jielu Li and Zhenchun Zang
Mathematics 2021, 9(21), 2657; https://doi.org/10.3390/math9212657 - 20 Oct 2021
Cited by 3 | Viewed by 1108
Abstract
The processing of a sparse matrix is a hot topic in the recommendation system. This paper applies the method of hesitant fuzzy set to study the sparse matrix processing problem. Based on the uncertain factors in the recommendation process, this paper applies hesitant [...] Read more.
The processing of a sparse matrix is a hot topic in the recommendation system. This paper applies the method of hesitant fuzzy set to study the sparse matrix processing problem. Based on the uncertain factors in the recommendation process, this paper applies hesitant fuzzy set theory to characterize the historical ratings embedded in the recommendation system and studies the data processing problem of the sparse matrix under the condition of a hesitant fuzzy set. The key is to transform the similarity problem of products in the sparse matrix into the similarity problem of two hesitant fuzzy sets by data conversion, data processing, and data complement. This paper further considers the influence of the difference of user ratings on the recommendation results and obtains a user’s recommendation list. On the one hand, the proposed method effectively solves the matrix in the recommendation system; on the other hand, it provides a feasible method for calculating similarity in the recommendation system. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Sets Theory and Their Extensions)
26 pages, 1950 KiB  
Article
A Hybrid Spherical Fuzzy MCDM Approach to Prioritize Governmental Intervention Strategies against the COVID-19 Pandemic: A Case Study from Vietnam
by Phi-Hung Nguyen, Jung-Fa Tsai, Thanh-Tuan Dang, Ming-Hua Lin, Hong-Anh Pham and Kim-Anh Nguyen
Mathematics 2021, 9(20), 2626; https://doi.org/10.3390/math9202626 - 18 Oct 2021
Cited by 37 | Viewed by 3521
Abstract
The unprecedented coronavirus pandemic (COVID-19) is fluctuating worldwide. Since the COVID-19 epidemic has a negative impact on all countries and has become a significant threat, it is necessary to determine the most effective strategy for governments by considering a variety of criteria; however, [...] Read more.
The unprecedented coronavirus pandemic (COVID-19) is fluctuating worldwide. Since the COVID-19 epidemic has a negative impact on all countries and has become a significant threat, it is necessary to determine the most effective strategy for governments by considering a variety of criteria; however, few studies in the literature can assist governments in this topic. Selective governmental intervention during the COVID-19 outbreak is considered a Multi-Criteria Decision-Making (MCDM) problem under a vague and uncertain environment when governments and medical communities adjust their priorities in response to rising issues and the efficacy of interventions applied in various nations. In this study, a novel hybrid Spherical Fuzzy Analytic Hierarchy Process (SF-AHP) and Fuzzy Weighted Aggregated Sum Product Assessment (WASPAS-F) model is proposed to help stakeholders such as governors and policymakers to prioritize governmental interventions for dealing with the COVID-19 outbreak. The SF-AHP is implemented to measure the significance of the criteria, while the WASPAS-F approach is deployed to rank intervention alternatives. An empirical case study is conducted in Vietnam. From the SF-AHP findings, the criteria of “effectiveness in preventing the spread of COVID-19”, “ease of implementation”, and “high acceptability to citizens” were recognized as the most important criteria. As for the ranking of strategies, “vaccinations”, “enhanced control of the country’s health resources”, “common health testing”, “formation of an emergency response team”, and “quarantining patients and those suspected of infection” are the top five strategies. Aside from that, the robustness of the approach was tested by performing a comparative analysis. The results illustrate that the applied methods reach the general best strategy rankings. The applied methodology and its analysis will provide insight to authorities for fighting against the severe pandemic in the long run. It may aid in solving many complicated challenges in government strategy selection and assessment. It is also a flexible design model for considering the evaluation criteria. Finally, this research provides valuable guidance for policymakers in other nations. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Sets Theory and Their Extensions)
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19 pages, 687 KiB  
Article
Distribution Linguistic Fuzzy Group Decision Making Based on Consistency and Consensus Analysis
by Feifei Jin, Chang Li, Jinpei Liu and Ligang Zhou
Mathematics 2021, 9(19), 2457; https://doi.org/10.3390/math9192457 - 02 Oct 2021
Cited by 3 | Viewed by 1500
Abstract
The development of distribution linguistic provides a new research idea for linguistic information group decision-making (GDM) problems, which is more flexible and convenient for experts to express their opinions. However, in the process of using distribution linguistic fuzzy preference relations (DLFPRs) to solve [...] Read more.
The development of distribution linguistic provides a new research idea for linguistic information group decision-making (GDM) problems, which is more flexible and convenient for experts to express their opinions. However, in the process of using distribution linguistic fuzzy preference relations (DLFPRs) to solve linguistic information GDM problems, there are few studies that pay attention to both internal consistency adjustment and external consensus of experts. Therefore, this study proposes a fresh decision support model based on consistency adjustment algorithm and consensus adjustment algorithm to solve GDM problems with distribution linguistic data. Firstly, we review the concept of DLFPRs to describe the fuzzy linguistic evaluation information, and then we present the multiplicative consistency of DLFPRs and a new consistency measurement method based on the distance, and investigate the consistency adjustment algorithm to ameliorate the consistency level of DLFPRs. Subsequently, the consensus degree measurement is carried out, and a new consensus degree calculation method is put forward. At the same time, the consensus degree adjustment is taken the expert cost into account to make it reach the predetermined level. Finally, a distribution linguistic fuzzy group decision making (DLFGDM) method is designed to integrate the evaluation linguistic elements and obtain the final evaluation information. A case of the evaluation of China’s state-owned enterprise equity incentive model is provided, and the validity and superiority of the proposed method are performed by comparative analysis. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Sets Theory and Their Extensions)
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10 pages, 283 KiB  
Article
Comprehensive Interval-Induced Weights Allocation with Bipolar Preference in Multi-Criteria Evaluation
by Xu Jin, Ronald R. Yager, Radko Mesiar, Surajit Borkotokey and Lesheng Jin
Mathematics 2021, 9(16), 2002; https://doi.org/10.3390/math9162002 - 21 Aug 2021
Cited by 3 | Viewed by 1937
Abstract
Preferences-involved evaluation and decision making are the main research subjects in Yager’s decision theory. When the involved bipolar preferences are concerned with interval information, some induced weights allocation and aggregation methods should be reanalyzed and redesigned. This work considers the multi-criteria evaluation situation [...] Read more.
Preferences-involved evaluation and decision making are the main research subjects in Yager’s decision theory. When the involved bipolar preferences are concerned with interval information, some induced weights allocation and aggregation methods should be reanalyzed and redesigned. This work considers the multi-criteria evaluation situation in which originally only the interval-valued absolute importance of each criterion is available. Firstly, based on interval-valued importance, upper bounds, lower bounds, and the mean points of each, we used the basic unit monotonic function-based bipolar preference weights allocation method four times to generate weight vectors. A comprehensive weighting mechanism is proposed after considering the normalization of the given absolute importance information. The bipolar optimism–pessimism preference-based weights allocation will also be applied according to the magnitudes of entries of any given interval input vector. A similar comprehensive weighting mechanism is still performed. With the obtained weight vector for criteria, we adopt the weighted ordered weighted averaging allocation on a convex poset to organically consider both two types of interval-inducing information and propose a further comprehensive weights allocation mechanism. The detailed comprehensive evaluation procedures with a numerical example for education are presented to show that the proposed models are feasible and useful in interval, multi-criteria, and bipolar preferences-involved decisional environments. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Sets Theory and Their Extensions)
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