Almost bi-quasi-ideals and their fuzzifications in semigroups

Abstract

The notion of bi-quasi-ideals of semigroups was introduced by Krishna Rao in 2017, which is a generalization of left ideals, right ideals, bi-ideals, and quasi-ideals of semigroups. In this paper, we introduce the concept of almost bi-quasi ideals as a generalization of bi-quasi ideals of semigroups. We investigate the properties of almost bi-quasi-ideals and fuzzy almost bi-quasi-ideals in semigroups. Moreover, we show some relationships between almost bi-quasi-ideals and fuzzy almost bi-quasi-ideals.