On some algebraic aspects of η-intuitionistic fuzzy subgroups

Abstract

In this study, we presents the idea of η-intuitionistic fuzzy subgroup (IFSG) defined on ηintuitionistic fuzzy set (IFS). Furthermore, we prove that every IFSG is an η-IFSG. Also, we extend the study of this notion to define η-intuitionistic fuzzy cosets and η-intuitionistic fuzzy normal subgroups of a given group and investigate some of their fundamental algebraic features. Besides, we define the η-intuitionistic fuzzy homomorphism between two η-IFSG's and show that an η-intuitionistic fuzzy homomorphic image (inverse image) of the η-IFSG is an η-IFSG.

t-Intuitionistic Fuzzy Structures on PMS-Ideals of a PMS-Algebra

“…Sharma [17,18] developed the concept of the t-intuitionistic fuzzy set as an extension of the intuitionistic fuzzy set to deal with uncertainty and vagueness within the context of some reference points in the unit interval [0,1] and then introduced the concepts of t-intuitionistic fuzzy subgroups and t-intuitionistic fuzzy subrings. Shuaib et al [19] introduced the notion of η-intuitionistic fuzzy subgroup over η-intuitionistic fuzzy subset and studied some algebraic aspects of η-fuzzy subgroups. Barbhuiya [20] introduced the notion of t-intuitionistic fuzzy subalgebra and t-intuitionistic fuzzy normal subalgebra of BG-algebra and studied their properties.…”

A Novel Applications of Complex Intuitionistic Fuzzy Sets in Group Theory

“…Garg and Rani [31][32][33][34][35] made remarkable effort to extend the notion of intuitionistic fuzzy sets in decision making problems. Shuaib et al [36] explored some fundamental algebraic properties of η-intuitionistic fuzzy subgroups. Shuaib et al [37] discussed some more characterization of ξ-intuitionistic fuzzy subgroups.…”

“…Shuaib et al [36] explored some fundamental algebraic properties of η-intuitionistic fuzzy subgroups. Shuaib et al [37] discussed some more characterization of ξ-intuitionistic fuzzy subgroups. The new development about Γ-interval valued fuzzification of Lagrange's theorem of Γ interval valued fuzzy subgroups was studied in [38].…”

Algebraic Characteristics of Anti-Intuitionistic Fuzzy Subgroups Over a Certain Averaging Operator

“…Kausar [30] proposed the concept of direct product of finite intuitionistic anti fuzzy normal subrings over non-associative rings in 2019. For more on intuitionistic fuzzy sets, we suggest reading of [31][32][33][34][35][36][37][38][39][40].…”