Fuzzy Sets Theory and Its Applications

Topic Information

Dear Colleagues,

The concept of fuzzy sets introduced by L.A. Zadeh in 1965 tried 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 membership functions associated with a fuzzy set, each element in a set allows one to take any values between 0 and 1 that can be treated as the degree of membership. This kind of imprecision draws forth a multitude of applications. This topic will focus on the original research that reflects the theoretical developments and applicable results.

The topics of interest include but are not limited to the following:

• Foundation of fuzzy sets (fuzzy arithmetic operations, extension principle, 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.). 
• Nature of computation (ant colony optimization, artificial immune systems, genetic algorithms, particle swarm intelligence, simulated annealing, tabu search, etc.). 
• Computational intelligence (artificial intelligence, approximate reasoning, expert systems, machine learning, support vector machines, robotics, image processing, pattern recognition, information retrieval, etc.). 
• Operations research and management sciences (fuzzy games theory, fuzzy inventory models, fuzzy queueing theory, fuzzy scheduling problems, fuzzy optimization, fuzzy decision making, fuzzy data mining, fuzzy clustering, stochastic optimization, financial derivatives, uncertainty modeling, etc.).

Prof. Dr. Hsien-Chung Wu
Prof. Dr. Ziye Zhang
Dr. Rongrong Yu
Topic Editors

Keywords

Participating Journals

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
Algorithms algorithms	2.1	4.5	2008	17.8 Days	CHF 1800	Submit
Axioms axioms	1.6	-	2012	21.6 Days	CHF 2400	Submit
Energies energies	3.2	7.3	2008	16.2 Days	CHF 2600	Submit
Mathematics mathematics	2.2	4.6	2013	18.4 Days	CHF 2600	Submit
Symmetry symmetry	2.2	5.3	2009	17.1 Days	CHF 2400	Submit

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Published Papers (2 papers)

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All Algorithms Axioms Energies Mathematics Symmetry

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28 pages, 418 KiB  

Open AccessArticle

Geometric Accumulation Operators of Dombi Weighted Trapezoidal-Valued Fermatean Fuzzy Numbers with Multi-Attribute Group Decision Making

by M. Kaviyarasu, J. Angel and Mohammed Alqahtani

Symmetry 2025, 17(7), 1114; https://doi.org/10.3390/sym17071114 - 10 Jul 2025

Abstract

Trapezoidal-valued fermatean fuzzy numbers (TpVFFNs) are essential for handling daily decision-making issues in the engineering and management fields. Accumulation processes on the set of TpVFFN are used to address decision-making problems described in this environment as necessary. The primary goal of this paper [...] Read more.

Trapezoidal-valued fermatean fuzzy numbers (TpVFFNs) are essential for handling daily decision-making issues in the engineering and management fields. Accumulation processes on the set of TpVFFN are used to address decision-making problems described in this environment as necessary. The primary goal of this paper is to provide the concept of Dombi t-norm $\left(D_{tn}\right)$- and Dombi t-conorm $\left(D_{tcn}\right)$-based accumulation operators on the class of TpVFFN, emphasizing how they behave symmetrically in aggregation processes to maintain consistency and fairness. To use s to illustrate mathematical circumstances, we first create a trapezoidal-valued fermatean fuzzy Dombi’s weighted geometric operator, hexagonal hybird geometric operator, fermatean fuzzy order weighted geometric operator. Second, we use a multi-attribute group decision-making (MAGDM) approach to compute the recommended accumulation operators. Finally, we demonstrate the potential practical application of the proposed decision-making problem related to the pink cab. Full article

(This article belongs to the Topic Fuzzy Sets Theory and Its Applications)

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30 pages, 2525 KiB  

Open AccessArticle

A Dynamic Threat Assessment Method for Multi-Target Unmanned Aerial Vehicles at Multiple Time Points Based on Fuzzy Multi-Attribute Decision Making and Fuse Intention

by Qianru Niu, Shuangyin Ren, Wei Gao and Chunjiang Wang

Mathematics 2025, 13(10), 1663; https://doi.org/10.3390/math13101663 - 19 May 2025

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Abstract

In response to the threat assessment challenge posed by unmanned aerial vehicles (UAVs) in air defense operations, this paper proposes a dynamic assessment model grounded in fuzzy multi-attribute decision making. First, a three-dimensional evaluation index system is established, encompassing capability, opportunity, and intention. [...] Read more.

In response to the threat assessment challenge posed by unmanned aerial vehicles (UAVs) in air defense operations, this paper proposes a dynamic assessment model grounded in fuzzy multi-attribute decision making. First, a three-dimensional evaluation index system is established, encompassing capability, opportunity, and intention. Quantification functions for assessing the threat level of each attribute are then designed. To account for the temporal dynamics of the battlefield, an innovative fusion approach is developed, integrating inverse Poisson distribution time weights with subjective–objective comprehensive weighting, thereby establishing a dynamic variable weight fusion mechanism. Among these, the subjective weights are determined by integrating the intention probability matrix, effectively incorporating the intentions into the threat assessment process to reflect their dynamic changes and enhancing the overall evaluation accuracy. Leveraging the improved technique for order preference by similarity to ideal solution (TOPSIS), the model achieves threat prioritization. Experimental results demonstrate that this method significantly enhances the reliability of threat assessments in uncertain and dynamic battlefield environments, offering valuable support for air defense command and control systems. Full article

(This article belongs to the Topic Fuzzy Sets Theory and Its Applications)

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