• Dr. G. Hariprakash

The object of the work discussed in this paper is about the classes of fuzzy Green's relations. The aim of this study is to characterize the ‘transformation semigroups’ and ‘semigroups of transformations’ using fuzzy property to get semigroups of fuzzy transformations and transformation fuzzy subsemigroups. In particular a subsemigroup of classes of fuzzy Green's relations is considered to introduce a semigroup of Green's fuzzy transformations. Any of its subgroup is defined as a fuzzy transformation subsemigroup. Based on these concepts six prepositions are established to find out a theorem stating equivalent conditions of strictly idempotent separating fuzzy congruence equivalence relations on a generalized inverse semigroup. From three theorems, state a Green's fuzzy idempotent separating fuzzy relation between two elements of a generalized inverse semigroup. The study concludes by establishing this fuzzy relation as a fuzzy congruence. As a result, a new notion is introduced by defining the fuzzy relation between these two elements called Green's fuzzy congruence of idempotent separating relation.

"GREEN’S FUZZY CONGRUENCE OF IDEMPOTENT SEPARATING FUZZY RELATION", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 5, page no.552-555, May-2019, Available :http://www.jetir.org/papers/JETIR1905975.pdf

"GREEN’S FUZZY CONGRUENCE OF IDEMPOTENT SEPARATING FUZZY RELATION", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 5, page no. pp552-555, May-2019, Available at : http://www.jetir.org/papers/JETIR1905975.pdf