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...