Algebraic Perspectives of Fuzzy Sets: Structures and Properties

Satabdi  Ray ¹ ( Department of Mathematics, National Institute of Technology, Agartala, Tripura, India. )
Debnarayan  Khatua ² ( Department of mathematics & Statistics, Vignan’s Foundation for Science, Technology and Research, Guntur, India. )
Sayantan Mandal ³ ( Department of Basic Science and Humanities, Institute of Engineering and Management (IEM), University of Engineering and Management Kolkata, Kolkata, India. )

Submited date : 2024-11-26 Accepted date : 2025-05-15

Keywords: Fuzzy set, Algebraic structure, Monoid, Semi-ring, Lattice, Semi-lattice, Near-ring, Anti-ring.,

Abstract :

A structure that is inherent to a specific space and involves actions within that space is highly significant. Various types of structures regarding fuzzy sets have been extensively examined in the literature. Examples of these structures encompass algebraic, topological, and analytical structures. This study examines several algebraic structures present in the domain of fuzzy sets, specifically focusing on the standard union and intersection operations of fuzzy sets. Furthermore, we provide updated depictions for specific subspaces of fuzzy sets and introduce newly defined operations. Consequently, we examine different structures on different subspaces of fuzzy sets in connection to the just-mentioned operations.

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