On Classes of Green’s fuzzy Genaralized Inverse Semigroup

In the field of research, the study about fuzziness in the classes of regular semigroups becomes very important in the recent days. The fast and intensive development of the subject fuzzy relations has been continued from the twentieth century. In logical algebra using fuzzy tools many definitions related to fuzzy algebraic structure are established recently. In the paper “On Green’s Fuzzy Orthodox semigroup” (G Hariprakash, 2016) and “On Green’s fuzzy generalized inverse semigroup” G Hariprakash, 2017) characterizes orthodox semigroups and generalized inverse semigroups using fuzzy property. This work is a follow up of these studies. Mainly the work concentrated on classes of Green’s Fuzzy Orthodox semigroups and classes of Green’s Fuzzy Generalized inverse semigroups. In particular the study is about the quotient classes of Green’s Fuzzy Orthodox semigroups and quotient classes of Green’s Fuzzy Generalized inverse sEmigroups. The text includes two lammas in Green’s Fuzzy Generalized inverse semigroup and two lemmas in Green’s Fuzzy Orthodox semigroup. The conclusion of the work is to find out a necessary and sufficient condition for quotient classes of Green’s Fuzzy Regular semigroup to be a Green’s Fuzzy Orthodox semigroup. This work endeavors the opening of a new area of study Green’s Fuzzy Idempotent Separating, Krenal of Green’s Fuzzy relations and other related notions.