Almost phi-fuzzy semi-ideals in groupoids

Abstract

In this paper, we introduce the notions of an almost phi-fuzzy subalgebra and an almost phi-fuzzy semi-ideal in groupoids by using the concept of a function. This concepts are generalizations of a fuzzy subalgebra and a fuzzy ideal in groupoids respectively. We discuss some relations between almost phi-fuzzy subalgebras and vanishing, level subsets. By introducing the notions of (mu, phi)-extremes, e-ideals, we obtain several properties of almost phi-fuzzy subalgebras. The relations between almost phi-fuzzy semi-ideals and (mu, phi)-special elements are discussed. Finally we discuss fuzzy algebraic structures of almost phi-fuzzy semi-ideals by diagrams.