On Weakly Regular Semigroups Characterized in Terms of Generalized Interval-Valued Fuzzy Subsemigroups

Abstract

In this paper, we give definitions of generalized interval-valued fuzzy subsemigroups, which are generalizations of the concept of interval-valued fuzzy subsemigroups, and of $(\overline{\alpha}, \overline{\beta})$-interval-valued fuzzy subsemigroups, where $\overline{\alpha} \prec \overline{\beta}$. The relations between the generalized interval fuzzy subsemigroups and various subsemigroups are discussed. The main result is a characterization of weakly regular semigroups by using the properties of these generalized interval-valued fuzzy subsemigroups of semigroups.