Fuzzy admissible congruences on type B semigroups with E-properties, and their applications

Abstract

Type B semigroups are described as the generalized inverse semigroups in the range of abundant semigroup. Motivated by studying fuzzy congruences in inverse semigroups, and as a continuation of N. Kuroki’s work in inverse semigroups and our work in abundant semigroups in terms of fuzzy subsets, this paper considers fuzzy admissible congruences on some classes of type B semigroups. Our main purpose is to show when a fuzzy admissible congruence on a type B semigroup with E-properties is E-properties preserving. In particular, we get some sufficient and necessary conditions for some classes of type B semigroups to be primitive, E-unitary and E-reflexive, respectively. As an application, we extend our results to the cases of inverse semigroups.