The Lattices of Group Fuzzy Congruences and Normal Fuzzy Subsemigroups on E

The aim of this paper is to investigate the lattices of group fuzzy congruences and normal fuzzy subsemigroups on E-inversive semigroups. We prove that group fuzzy congruences and normal fuzzy subsemigroups determined each other in E-inversive semigroups. Moreover, we show that the set of group t-fuzzy congruences and the set of normal subsemigroups with tip t in a given E-inversive semigroup form two mutually isomorphic modular lattices for every t∈0,1

Some intuitionistic fuzzy congruences

First, we introduce the concept of intuitionistic fuzzy group congruence and we obtain the characterizations of intuitionistic fuzzy group congruences on an inverse semigroup and a T * -pure semigroup, respectively. Also, we study some properties of intuitionistic fuzzy group congruence. Next, we introduce the notion of intuitionistic fuzzy semilattice congruence and we give the characterization of intuitionistic fuzzy semilattice congruence on a T * -pure semigroup. Finally, we introduce the concept of intuitionistic fuzzy normal congruence and we prove that (IFNC(E S ), ∩, ∨) is a complete lattice. And we find the greatest intuitionistic fuzzy normal congruence containing an intuitionistic fuzzy congruence on E S

A Study of G-Fuzzy Congruence Relations

Many authors studied on the fuzzy counterpart of Group Theory, since Rosenfeld. But, there is little literature on Fuzzy Semigroups. Here the authors try to extend the fuzzy congruence relations to Semi groups