Author: Diwakar Prasad Baranwal
DOI Link: https://doi.org/10.70798/Bijmrd/04010038
Abstract: Fuzzy group theory extends classical group theory by allowing graded membership and thereby provides a rigorous algebraic framework for modeling uncertainty and partial symmetry. Among the fundamental concepts in this theory, fuzzy normal subgroups play a central role in the construction of quotient fuzzy groups and in the formulation of fuzzy homomorphism theorems. This paper investigates intrinsic structural properties of fuzzy normal subgroups and quotient fuzzy groups, with particular emphasis on membership-based characterizations that do not rely solely on level-set techniques. New equivalence conditions for fuzzy normality are established, and refined quotient constructions are analyzed to clarify the behavior of fuzzy membership functions on factor groups. In addition, extensions of classical isomorphism theorems are obtained under weaker assumptions expressed in terms of fuzzy membership and support conditions. These results contribute to a deeper understanding of quotient structures in fuzzy group theory and strengthen the algebraic foundations of fuzzy algebra.
Keywords: Fuzzy groups; Fuzzy normal subgroups; Quotient fuzzy groups; Fuzzy homomorphisms; Isomorphism theorems; Fuzzy algebra.
Page No: 277-287