Generalized fuzzy Abel Grassmann's Groupoids
Fuzzy semigroup theory concentrates on theoretical aspects, but also includes applications in the areas of fuzzy coding theory, fuzzy finite state machines, and fuzzy languages. In this paper, we introduce the concept of (a, beta) -fuzzy hi-ideals in AG-groupoids. Using the notion of "belongingness (is an element of)" and "quasi coincidence(q)" of fuzzy points with fuzzy sets, we introduce the concept of an (a, beta)-fuzzy hi-ideals of an AG-groupoid G, where(alpha, beta is an element of {is an element of, q, is an element of boolean OR q, is an element of boolean AND q}) with alpha not equal is an element of boolean AND q. Since the concept of (is an element of, is an element of boolean OR q)-fuzzy bi-ideal is an important and useful generalization of ordinary fuzzy bi-deal, we discuss some fundamental aspects of (is an element of, is an element of boolean OR q)-fuzzy bi-ideals and ((is not an element of) over bar, (is not an element of) over bar boolean OR q)-fuzzy bi-ideals. A fuzzy subset F of an AG-groupoid G is an (is an element of, is an element of boolean OR q)-fuzzy bi-ideal if and only if F(lambda), the level cut of F is a bi-ideal of G, for all lambda is an element of(0, 0.5] and F is an ((is not an element of) over bar, (is not an element of) over bar boolean OR (q) over bar)-fuzzy hi-ideal if and only if F(lambda), is a bi-ideal of G, for all lambda is an element of(0, 0.5]. This means that an (is an element of, is an element of boolean OR q)-fuzzy bi-ideals and ((is not an element of) over bar, (is not an element of) over bar boolean OR (q) over bar)-fuzzy bi-ideals are generalizations of the existing concept of fuzzy bi-ideals. We characterize regular AG-groupoid in terms of a fuzzy right and a fuzzy left ideal.
ag-groupoid bi-ideals fuzzy subsets regular ag-groupoids fuzzy bi-ideals (alpha, beta) -fuzzy bi-ideals (is an element of, is an element of boolean or q) -fuzzy bi-ideals ((is an element of)over-bar, (is an element of)over-bar boolean or (q)over-bar) -fuzzy bi-ideals