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A fuzzy subset f of a given set S is described as an arbitrary function f: S→ 0, 1, where 0, 1 is the usual closed interval of real numbers. This fundamental concept was first introduced by Zadeh in his pioneering paper 1 of 1965, which provides a natural framework for the generalizations of some basic notions of algebra, for example, set theory, group theory, ring theory, groupoids, real analysis, measure theory, topology, and differential equations, and so forth. Rosenfeld see 2 was the first who introduced the concept of a fuzzy set in a group. The concept of a fuzzy ideal in semigroups was first developed by Kuroki see 3–8. He studied fuzzy ideals, fuzzy bi-ideals, fuzzy quasi-ideals, and fuzzy semiprime ideals of semigroups. Fuzzy ideals and Green’s relations in semigroups were studied by McLean and Kummer in 9. Dib and Galham in 10 introduced the definitions of a fuzzy groupoid and a fuzzy semigroup and studied fuzzy ideals and fuzzy bi-ideals of a fuzzy semigroup. Ahsan et al. in 11 characterized semisimple semigroups in terms of fuzzy ideals. A systematic exposition of fuzzy semigroups by Mordeson et al. appeared in 12, where one can find theoretical results on fuzzy semigroups and their use in fuzzy coding, fuzzy finite state machines, and fuzzy languages. The monograph by Mordeson and Malik see 13 deals with the applications of fuzzy approach to the concept of automata and formal languages. Fuzzy sets in ordered semigroups/ordered groupoids were first introduced by Kehayopulu