Intuitionistic $(S,T)$-Fuzzy $M$-Subsemigroups of an $M$-Semigroup

Abstract:

      Intuitionistic fuzzy sets are generalized fuzzy sets which were first introduced by Atanassov in 1986. In this paper, we introduce the concept of intuitionistic fuzzy $M$-subsemigroups of an $M$-semigroup $M$ with respect to an $s$-norm $S$ and a $t$-norm $T$ on intuitionistic fuzzy sets and study their properties. In particular, intuitionistic $(S,T)$-direct products of $M$-semigroups are considered and some recent results of fuzzy $M$-subsemigroups of $M$-semigroups obtained by Zhan and Tan$^{[21]}$ are extended and generalized to intuitionistic $(S,T)$-fuzzy $M$-subsemigroups over $M$-semigroups.