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Axioms
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New Perspectives in Fuzzy Sets and Their Applications, 2nd Edition
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New Perspectives in Fuzzy Sets and Their Applications, 2nd Edition

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

Deadline for manuscript submissions: 31 May 2025 | Viewed by 1907

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 classical set theory. It is well known that a classical set corresponds to an indicator function whose values only take 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 time 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

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Published Papers (3 papers)

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27 pages, 508 KiB  
Article
Spherical Fuzzy Credibility Dombi Aggregation Operators and Their Application in Artificial Intelligence
by Neelam Khan, Muhammad Qiyas, Darjan Karabasevic, Muhammad Ramzan, Mubashir Ali, Igor Dugonjic and Dragisa Stanujkic
Axioms 2025, 14(2), 108; https://doi.org/10.3390/axioms14020108 - 31 Jan 2025
Viewed by 549
Abstract
It was recently proposed to extend the spherical fuzzy set to spherical fuzzy credibility sets (SFCSs). In this paper, we define the concept of SFCSs. We then define new operational laws for SFCSs using Dombi operational laws. Various spherical fuzzy credibility aggregation operators [...] Read more.
It was recently proposed to extend the spherical fuzzy set to spherical fuzzy credibility sets (SFCSs). In this paper, we define the concept of SFCSs. We then define new operational laws for SFCSs using Dombi operational laws. Various spherical fuzzy credibility aggregation operators such as spherical fuzzy credibility Dombi weighted averaging (SFCDWA), spherical fuzzy credibility Dombi ordered weighted averaging (SFCDOWA), spherical fuzzy credibility Dombi weighted geometric (SFCDWG), and spherical fuzzy credibility Dombi ordered weighted geometric (SFCDOWG) are defined. We also show the boundedness, monotonicity, and idempotency aspects of the suggested operators. We proposed the spherical fuzzy credibility entropy to find the unknown weight information of the attributes. Symmetry analysis is a useful and important tool in artificial intelligence that may be used in a variety of fields. To calculate the significant factor, we determine the multi-attribute decision-making (MADM) method using the suggested operators for SFCSs to increase the value of the assessed operators. To demonstrate the effectiveness and superiority of the suggested approach, we compare our findings to those of many other approaches. Full article
(This article belongs to the Special Issue New Perspectives in Fuzzy Sets and Their Applications, 2nd Edition)
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15 pages, 1353 KiB  
Article
Similarity of Overlap Functions and Robustness of Fuzzy Reasoning
by Songsong Dai and Qiuchen Ruan
Axioms 2025, 14(1), 45; https://doi.org/10.3390/axioms14010045 - 7 Jan 2025
Viewed by 476
Abstract
The overlap function has been extensively utilized across various fields. In this paper, we introduce the concepts of the similarity and δ-equality of overlap functions to measure the degree of similarity between two overlap functions. Subsequently, we examine the δ-equality of [...] Read more.
The overlap function has been extensively utilized across various fields. In this paper, we introduce the concepts of the similarity and δ-equality of overlap functions to measure the degree of similarity between two overlap functions. Subsequently, we examine the δ-equality of several operations on overlap functions, including meet, join, and weighted sum, to assess how these operations maintain the similarity. Finally, we discuss the robustness of fuzzy reasoning for FMP, FMT, and FHS models based on the δ-equality of the overlap functions. Full article
(This article belongs to the Special Issue New Perspectives in Fuzzy Sets and Their Applications, 2nd Edition)
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26 pages, 4050 KiB  
Systematic Review
A Systematic Overview of Fuzzy-Random Option Pricing in Discrete Time and Fuzzy-Random Binomial Extension Sensitive Interest Rate Pricing
by Jorge de Andrés-Sánchez
Axioms 2025, 14(1), 52; https://doi.org/10.3390/axioms14010052 - 10 Jan 2025
Viewed by 544
Abstract
Since the early 2000s, fuzzy mathematics has fostered a stream of research on the financial valuation of assets incorporating optionality. This paper makes two contributions to this field. First, it conducts a bibliographical analysis of contributions from fuzzy set theory to option pricing, [...] Read more.
Since the early 2000s, fuzzy mathematics has fostered a stream of research on the financial valuation of assets incorporating optionality. This paper makes two contributions to this field. First, it conducts a bibliographical analysis of contributions from fuzzy set theory to option pricing, focusing on fuzzy-random option pricing (FROP) and its applications in binomial and trinomial lattice approaches. Second, it extends the FROP to yield curve modeling within a binomial framework. The bibliographical analysis followed the PRISMA guidelines and was conducted via the SCOPUS and WoS databases. We present a structured review of papers on FROP in discrete time (FROPDT), identifying the principal papers and outlets. The findings reveal that this focus has been applied to price options on stocks, stock indices, and real options. However, the exploration of its application to the term structure of interest-sensitive interest rate assets is very rare. To address this gap, we develop a fuzzy-random extension of the Ho–Lee term structure model, applying it to the European interbank market and price caplet options. Full article
(This article belongs to the Special Issue New Perspectives in Fuzzy Sets and Their Applications, 2nd Edition)
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