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 $\left[\mathrm{0,1}\right]$ . 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.