The lattice of intuitionistic fuzzy congruences

Abstract

First, we prove that the set of intuitionistic fuzzy congruences on a semigroup satisfying the particular condition is a modular lattice [Theorem 2.9]. Secondly, we prove that the set of all intuitionistic fuzzy congruences on a regular semigroup contained in (χH, χHc) forms a modular lattice [Proposition 3.5]. And also we show that the set of all intuitionistic fuzzy idempotent separating congruences on a regular semigroup forms a modular lattice[Theorem 3.6]. Moreover, we prove that the lattice of intuitionistic fuzzy congruences on a regular semigroup is a disjoint union of some modular sublattices of the lattice[Corollary 3.15]. Finally, we show that the lattice of intuitionistic fuzzy congruences on a group and the lattice of intuitionistic fuzzy normal subgroups satisfying the particular condition are lattice isomorphic[Theorem 4.6]. Corresponding author 212 Kul Hur, Su Youn Jang and Hee Won Kang Mathematics Subject Classification: 03F55, 06B10, 06C05