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Axioms
Special Issues
New Perspectives in Fuzzy Sets and Its Applications
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New Perspectives in Fuzzy Sets and Its Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Logic".

Deadline for manuscript submissions: 31 May 2024 | Viewed by 4878

Special Issue Editor

Prof. Dr. Hsien-Chung Wu

E-Mail Website
Guest Editor
Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan
Interests: fuzzy sets; optimization; nonlinear analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The concept of fuzzy sets was first introduced by L.A. Zadeh in 1965, in an attempt to extend the classical set theory. It is well known that a classical set corresponds to an indicator function whose values are only taken to be 0 and 1. With the aid of a membership function associated with a fuzzy set, each element in a set can allow any value between 0 and 1 to be regarded as the degree of membership. This imprecision draws forth a multitude of applications. This Special Issue welcomes the submission of original research articles that reflect theoretical developments and applicable results. The topics of interest include, but are not limited to, the following:

  • Foundations of fuzzy sets (fuzzy arithmetic operations, extension principle, gradual sets and gradual elements, possibility measures, etc.);
  • Fuzzy mathematics (fuzzy topology, fuzzy real analysis, fuzzy integral and differential equations, fuzzy metric spaces, fuzzy algebra, etc.);
  • Fuzzy logics (many-valued logics, type-2 fuzzy logics, intuitionistic fuzzy logics, etc.);
  • Fuzzy statistical analysis (fuzzy random variables, fuzzy regression analysis, fuzzy reliability analysis, fuzzy times series, fuzzy Markov process, etc.);
  • Hybrid systems (fuzzy control, fuzzy neural networks, genetic fuzzy systems, fuzzy intelligent systems, fuzzy biomedical systems, fuzzy chaotic systems, fuzzy information systems, etc.);

Operations research and management sciences (fuzzy games theory, fuzzy inventory models, fuzzy queueing theory, fuzzy scheduling problems, fuzzy decision-making, fuzzy data mining, fuzzy clustering, etc.).

Prof. Dr. Hsien-Chung Wu
Guest Editor

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. Axioms is an international peer-reviewed open access monthly 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 2400 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 sets
  • fuzzy logic
  • fuzzy optimization
  • fuzzy systems
  • extension principle
  • gradual sets

Published Papers (6 papers)

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Research

14 pages, 287 KiB  
Article
On Proximity Spaces Constructed on Rough Sets
by Jong Il Baek, S. E. Abbas, Kul Hur and Ismail Ibedou
Axioms 2024, 13(3), 199; https://doi.org/10.3390/axioms13030199 - 15 Mar 2024
Viewed by 676
Abstract
Based on equivalence relation R on X, equivalence class [x] of a point and equivalence class [A] of a subset represent the neighborhoods of x and A, respectively. These neighborhoods play the main role in defining separation [...] Read more.
Based on equivalence relation R on X, equivalence class [x] of a point and equivalence class [A] of a subset represent the neighborhoods of x and A, respectively. These neighborhoods play the main role in defining separation axioms, metric spaces, proximity relations and uniformity structures on an approximation space (X,R) depending on the lower approximation and the upper approximation of rough sets. The properties and the possible implications of these definitions are studied. The generated approximation topology τR on X is equivalent to the generated topologies associated with metric d, proximity δ and uniformity U on X. Separated metric spaces, separated proximity spaces and separated uniform spaces are defined and it is proven that both are associating exactly discrete topology τR on X. Full article
(This article belongs to the Special Issue New Perspectives in Fuzzy Sets and Its Applications)
28 pages, 1770 KiB  
Article
Fitting Insurance Claim Reserves with Two-Way ANOVA and Intuitionistic Fuzzy Regression
by Jorge De Andrés-Sánchez
Axioms 2024, 13(3), 184; https://doi.org/10.3390/axioms13030184 - 11 Mar 2024
Viewed by 786
Abstract
A highly relevant topic in the actuarial literature is so-called “claim reserving” or “loss reserving”, which involves estimating reserves to be provisioned for pending claims, as they can be deferred over various periods. This explains the proliferation of methods that aim to estimate [...] Read more.
A highly relevant topic in the actuarial literature is so-called “claim reserving” or “loss reserving”, which involves estimating reserves to be provisioned for pending claims, as they can be deferred over various periods. This explains the proliferation of methods that aim to estimate these reserves and their variability. Regression methods are widely used in this setting. If we model error terms as random variables, the variability of provisions can consequently be modelled stochastically. The use of fuzzy regression methods also allows modelling uncertainty for reserve values using tools from the theory of fuzzy subsets. This study follows this second approach and proposes projecting claim reserves using a generalization of fuzzy numbers (FNs), so-called intuitionistic fuzzy numbers (IFNs), through the use of intuitionistic fuzzy regression. While FNs allow epistemic uncertainty to be considered in variable estimation, IFNs add bipolarity to the analysis by incorporating both positive and negative information regarding actuarial variables. Our analysis is grounded in the ANOVA two-way framework, which is adapted to the use of intuitionistic regression. Similarly, we compare our results with those obtained using deterministic and stochastic chain-ladder methods and those obtained using two-way statistical ANOVA. Full article
(This article belongs to the Special Issue New Perspectives in Fuzzy Sets and Its Applications)
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14 pages, 592 KiB  
Article
On Equivalence Operators Derived from Overlap and Grouping Functions
by Lei Du, Yingying Xu, Haifeng Song and Songsong Dai
Axioms 2024, 13(2), 123; https://doi.org/10.3390/axioms13020123 - 17 Feb 2024
Viewed by 701
Abstract
This paper introduces the concept of equivalence operators based on overlap and grouping functions where the associativity property is not strongly required. Overlap functions and grouping functions are weaker than positive and continuous t-norms and t-conorms, respectively. Therefore, these equivalence operators do not [...] Read more.
This paper introduces the concept of equivalence operators based on overlap and grouping functions where the associativity property is not strongly required. Overlap functions and grouping functions are weaker than positive and continuous t-norms and t-conorms, respectively. Therefore, these equivalence operators do not necessarily satisfy certain properties, such as associativity and the neutrality principle. In this paper, two models of fuzzy equivalence operators are obtained by the composition of overlap functions, grouping functions and fuzzy negations. Their main properties are also studied. Full article
(This article belongs to the Special Issue New Perspectives in Fuzzy Sets and Its Applications)
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18 pages, 1158 KiB  
Article
Integrating the Coupled Markov Chain and Fuzzy Analytic Hierarchy Process Model for Dynamic Decision Making
by Jih-Jeng Huang and Chin-Yi Chen
Axioms 2024, 13(2), 95; https://doi.org/10.3390/axioms13020095 - 30 Jan 2024
Viewed by 787
Abstract
This paper introduces a pioneering model that merges coupled Markov chains (CMC) with the fuzzy analytic hierarchy process (FAHP) to enhance multi-criteria decision making (MCDM) amidst the dynamic interplay of criteria. Traditional MCDM frameworks often lack the granularity to manage the intricate and [...] Read more.
This paper introduces a pioneering model that merges coupled Markov chains (CMC) with the fuzzy analytic hierarchy process (FAHP) to enhance multi-criteria decision making (MCDM) amidst the dynamic interplay of criteria. Traditional MCDM frameworks often lack the granularity to manage the intricate and changing relationships among criteria. Our model addresses this gap by integrating fuzzy numbers into AHP, providing a nuanced means to handle the inherent uncertainty of decision criteria. The application of the Kronecker product in CMC enriches our approach, offering a data-driven analysis while mitigating excessive dependence on subjective expert opinion. A comprehensive numerical example underlines the model’s improved decision-making accuracy and efficiency, marking a substantial advancement in MCDM methodologies. This research contributes to the field by presenting a sophisticated yet practical framework for dynamic decision analysis in complex uncertain environments. Full article
(This article belongs to the Special Issue New Perspectives in Fuzzy Sets and Its Applications)
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18 pages, 825 KiB  
Article
Ranking Alternatives Using a Fuzzy Preference Relation-Based Fuzzy VIKOR Method
by Hanh-Thao Le and Ta-Chung Chu
Axioms 2023, 12(12), 1079; https://doi.org/10.3390/axioms12121079 - 24 Nov 2023
Viewed by 741
Abstract
The process of evaluating and ranking alternatives, including the aggregation of various qualitative and quantitative criteria and weights of criteria, can be recognized as a fuzzy multiple criteria decision-making (MCDM) problem. In fuzzy MCDM problems, qualitative criteria and criteria weights are usually indicated [...] Read more.
The process of evaluating and ranking alternatives, including the aggregation of various qualitative and quantitative criteria and weights of criteria, can be recognized as a fuzzy multiple criteria decision-making (MCDM) problem. In fuzzy MCDM problems, qualitative criteria and criteria weights are usually indicated in linguistic values expressed in terms of fuzzy numbers, and values under quantitative criteria are usually crisp numbers. How to properly aggregate them for evaluating and selecting alternatives has been an important research issue. To help decision-makers make the most suitable selection, this paper proposes a fuzzy preference relation-based fuzzy VIKOR method. VIKOR is a compromise ranking method to solve discrete MCDM problems in complex systems. In this study, the F-preference relation is applied to compare fuzzy numbers with their means to produce a single index of a dominance level while still maintaining fuzzy meaning of the original linguistic values. The inverse function is applied to obtain the defuzzification values of Beta 1–4 to assist in the completion of the proposed method, and formulas can be clearly derived to facilitate the ranking procedure. Introducing fuzzy preference relation into fuzzy VIKOR can simplify the calculation procedure for more efficient decision-making. The proposed method is new and has never been seen before. A numerical example and a comparison of the proposed method are conducted to show and verify its expedience and advantage. Full article
(This article belongs to the Special Issue New Perspectives in Fuzzy Sets and Its Applications)
33 pages, 367 KiB  
Article
Normed Space of Fuzzy Intervals and Its Topological Structure
by Hsien-Chung Wu
Axioms 2023, 12(10), 996; https://doi.org/10.3390/axioms12100996 - 22 Oct 2023
Viewed by 782
Abstract
The space, Ƒcc(R), of all fuzzy intervals in R cannot form a vector space. However, the space Ƒcc(R) maintains a vector structure by treating the addition of fuzzy intervals as a vector [...] Read more.
The space, Ƒcc(R), of all fuzzy intervals in R cannot form a vector space. However, the space Ƒcc(R) maintains a vector structure by treating the addition of fuzzy intervals as a vector addition and treating the scalar multiplication of fuzzy intervals as a scalar multiplication of vectors. The only difficulty in taking care of Ƒcc(R) is missing the additive inverse element. This means that each fuzzy interval that is subtracted from itself cannot be a zero element in Ƒcc(R). Although Ƒcc(R) cannot form a vector space, we still can endow a norm on the space Ƒcc(R) by following its vector structure. Under this setting, many different types of open sets can be proposed by using the different types of open balls. The purpose of this paper is to study the topologies generated by these different types of open sets. Full article
(This article belongs to the Special Issue New Perspectives in Fuzzy Sets and Its Applications)
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