Exploring the Foundations of Fuzzy Systems in Logic, Sets and Graphs

Badri Vishal Padamwar

Authors

Badri Vishal Padamwar Department of Mathematics, ISBM University, Raipur, India

Keywords:

Fuzzy Logic, Fuzzy Set Theory, Fuzzy Graph Theory, Decision Making Systems, Intelligence Cycle, Applications, Fuzzy Systems, Trends, Overview

Abstract

This review article offers a comprehensive exploration of the intricate foundations of fuzzy systems, encompassing their integration into logic, sets, and graphs. Drawing insights from seminal works by Animesh Kumar Sharma, Lotfi A. Zadeh, and other notable researchers, the study aims to provide a nuanced understanding of the multifaceted landscape of fuzzy systems. The focal point is on trends in fuzzy graphs, applications of fuzzy logic and fuzzy set theory, and the conceptual framework of fuzzy graph theory. The review seeks to weave together diverse perspectives to shed light on the evolution and applications of these fundamental theories. The analysis begins with a critical examination of Sharma et al.'s work on trends in fuzzy graphs (2013), elucidating evolving patterns within fuzzy graph theory. Complementing this, Zadeh's foundational contributions to fuzzy logic (Zadeh, 2023) provide a historical context, offering a panoramic view of the development of fuzzy systems. The study seamlessly integrates recent advancements, such as the application of complex Dombi fuzzy graphs in decision-making problems (Butt et al., 2022) and the computation of domination sets in intuitionistic fuzzy graphs (Bozhenyuk et al., 2021). By incorporating a diverse array of references, ranging from foundational works to contemporary studies, this review aspires to encompass the breadth and depth of the fuzzy systems domain, offering a comprehensive synthesis of the foundational elements and modern developments in fuzzy logic, fuzzy set theory, and fuzzy graph theory.

References

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