CHARACTERIZATIONS OF MONOIDS BY THE PROPERTIES OF THEIR INTUITIONISTIC FUZZY SUBACTS

In this paper, we initiate the study of intuitionistic fuzzy subacts of an S-act, where S is a monoid with zero and S-acts are representations of S. We introduce the notions of pure intuitionistic fuzzy, purely intuitionistic maximal and purely intuitionistic fuzzy prime ideals of a monoid. It is shown that the set of purely intuitionistic fuzzy prime ideals of S admits the structure of a topological space, called the pure intuitionistic fuzzy spectrum of S. We also define a pure intuitionistic fuzzy subact of an S-act and call an S-act intuitionistic fuzzy normal if each of its intuitionistic fuzzy subact is pure. Monoids, of which all S-acts are intuitionistic fuzzy normal, are characterized. It is shown among other results that such monoids are right weakly regular.