The purpose of this thesis is to investigate some aspects of fuzzification of semigroups, partially ordered semigroups and gamma semigroups. In this thesis the concepts of fuzzy subsemigroups, fuzzy bi-ideals, fuzzy (1,2)-ideals, fuzzy quasi ideals, fuzzy ideals, fuzzy interior ideals, fuzzy prime and fuzzy semiprime ideals, cartesian product of fuzzy ideals, fuzzy prime ideals and fuzzy semiprime ideals, fuzzy ideal extensions in a gamma semigrouop have been introduced. These concepts are also studied via operator semigroups of a gamma semigroup. In this thesis some results of gamma semigroups have been rediscovered in terms of fuzzy subsets. Here some important characterization theorems in terms of fuzzy subsets have been obtained. It is important to note here that in the study of gamma semigroups in terms of fuzzy subsets operator semigroups play a crucial role.

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