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

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 ourwork in abundant semigroups in terms of fuzzy subsets, this paper considers fuzzy admissible congruences on some classes of typeBsemigroups. Our main purpose is to showwhen a fuzzy admissible congruence on a typeBsemigroup withE-properties isE-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.