Idempotent separating fuzzy conguences

This work mainly focuses on the developmental study of special classes of fuzzy relations. The discussion of fuzzy orthodox semigroups, as a special class of fuzzy relations, the combination and rearrangement of the idempotent elements of any concerned subject are significant in this work. So the extension of the study of fuzzy Green's relations (G.Hariprakash, 2016), to the area of fuzzy generalized inverse semigroup becomes more relevant. As a part and the course of development, this work, consider equivalence relations introduced by Yamada (M. Yamada, 1967) and the set of fuzzy congruences on semigroups. For more descriptive study of the subject along with the defined descriptions (G.Hariprakash, 2016), (G.Hariprakash,2016),(G.Hariprakash, 2017) a necessary and sufficient condition of idempotent separating fuzzy congruences, and a new notion called strictly idempotent separating fuzzy congruences is defined. Howie found out the greatest idempotent separating congruences on an inverse semigroup( J.M Howie,1976) and Kuroki introduced idempotent separating fuzzy congruences on inverse semigroups. These results are used to define idempotent separating fuzzy congruences fuzzy Green's relations on an inverse semigroup (] J.P. Kim and D.R. Bae, 1997). Moreover, this work extends the concept of group fuzzy congruences to Green's fuzzy relations.