Homomorphisms of Lattice-Valued Intuitionistic Fuzzy Subgroup Type-3

Abstract

The lattice-valued intuitionistic fuzzy set was introduced by Gerstenkorn and Tepavcevi as a generalization of both the fuzzy set and the L -fuzzy set by incorporating membership functions, nonmembership functions from a nonempty set X to any lattice L , and lattice homomorphism from L to the interval 0,1 . In this article, lattice-valued intuitionistic fuzzy subgroup type-3 (LIFSG-3) is introduced. Lattice-valued intuitionistic fuzzy type-3 normal subgroups, cosets, and quotient groups are defined, and their group theocratic properties are compared with the concepts in classical group theory. LIFSG-3 homomorphism is established and examined in relation to group homomorphism. The research findings are supported by provided examples in each section.

Intuitionistic multi fuzzy ideals of near-rings

“…Fathi was the first to describe the notion intuitionistic fuzzy group (Fathi & Salleh, 2009) Consequently, the intuitionistic versions of groups, rings, ideals, modules, near-rings etc., have been established (Hur et al, 2005). Many researchers (Kausar & Waqar, 2019;Kousar et al, 2021Kousar et al, , 2022Riaz et al, 2022a) used intuitionistic fuzzy sets and developed different structures. These included triangular intuitionistic fuzzy linear programming, lattice-valued intuitionistic fuzzy subgroup type-3, algebraic codes over lattice-valued intuitionistic fuzzy type-3 submodules, codes over lattice-valued intuitionistic fuzzy set type-3, non-associative ordered semi-groups by intuitionistic fuzzy bi ideals.…”