New Advancements in Fuzzy Sets Theory, Generalizations and Applications

Dear Colleagues,

A few decades ago, probability theory was the primary mathematical tool available to experts dealing with uncertainty in scientific research, engineering, and everyday decision-making. Its strength lies in the ability to quantify randomness and support decision-making based on the likelihood of various outcomes. However, it gradually became evident that many real-world problems are not strictly related to randomness but rather to vagueness and imprecision—features inherent in natural human language. Expressions such as "near," "warm," "likely," or "almost certain" cannot be easily captured within the framework of classical probability. To address this gap, Professor Lotfi Zadeh introduced fuzzy set theory in 1965, marking a significant advancement in modeling imprecise and linguistically expressed information. The flexibility of membership values aligns more closely with human reasoning and perception. Over time, various extensions of fuzzy sets have been developed to handle increasingly complex forms of uncertainty: Type 1 Fuzzy Sets, Type 2 fuzzy Sets, Intuitionistic Fuzzy Sets, Pythagorean Fuzzy Sets, Fermatian Fuzzy Sets, etc. These advanced fuzzy models have enabled researchers and engineers to develop mathematical representations of systems where binary logic fails to capture the complexity of real-world phenomena. They facilitate the analysis and solution of problems expressed in natural language, thus bridging the gap between formal mathematical modeling and intuitive human reasoning. All this resulted in a wide range of possible applications, including medicine, industry, economics, decision-making, education, and programming.

Focus

This Special Issue aims to bring together cutting-edge research and novel developments in the theory of fuzzy sets, their generalizations, and a wide range of emerging applications. Emphasis will be placed on new mathematical foundations, generalized models (such as intuitionistic, hesitant, type-2, Pythagorean, Fermatean, and spherical fuzzy sets), as well as interdisciplinary approaches that extend the traditional boundaries of fuzzy logic. Contributions that propose innovative theoretical insights, as well as those that demonstrate practical implementations in real-world systems, are particularly encouraged.

Scope

The scope of this Special Issue includes, but is not limited to, the following topics:

• New theoretical developments in fuzzy set theory and logic;
• Generalizations of fuzzy sets (intuitionistic, interval-valued, hesitant, picture, type-2, q-rung, spherical, etc.);
• Fuzzy relations, measures, and operations;
• Uncertainty modeling and decision-making under vagueness;
• Applications in machine learning, data mining, and artificial intelligence;
• Fuzzy approaches in engineering, economics, healthcare, environmental sciences, and social sciences;
• Fuzzy MCMD (AHP/TOPSIS/VIKOR…);
• Hybrid models combining fuzzy sets with rough sets, soft sets, or probabilistic models.

Interdisciplinary contributions that explore the integration of fuzzy methodologies with new computing paradigms are also within the scope.

Purpose

The purpose of this Special Issue is to offer the opportunity to researchers, academics, and experts in the field to present recent theoretical advances on fuzzy sets and fuzzy logic and their generalization and applications in areas of decision-making, economy, education, medicine, and programming. Also, the purpose is to showcase recent theoretical progress and to bridge it with robust, interpretable applications as well as to consolidate methods that handle vagueness and linguistic information, provide guidelines for rigorous evaluation (noise/shift robustness, ablation studies), and release resources that facilitate reuse and comparison.

Connection with the existing literature

This Special Issue will build upon the strong theoretical foundations established in previous research, while also addressing existing gaps and opening up new directions. It will consolidate recent theoretical innovations and practical applications that are currently dispersed across various subfields and journals. In doing so, this Special Issue will not only reflect the state of the art but also define a coherent trajectory for future research in fuzzy set theory and its generalizations.

Dr. Dušan J. Simjanović
Dr. Nataša Milosavljević
Dr. Branislav M. Ranđelović
Guest Editors

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• fuzzy sets
• generalizations of fuzzy sets
• fuzzy logic
• fuzzy numbers
• fuzzy AHP and generalizations
• all real-life applications