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This book mainly focuses on some aspects of semigroups and -semigroups related with different ideals as well as their various generalizations including fuzzyfication and intuitionistic fuzzyfication. The notions of characteristic ideals, fuzzy characteristic ideals, generalized bi-ideals, fuzzy generalized bi-ideals, intuitionistic fuzzy generalized bi-ideals, radicals of fuzzy ideals and fuzzy primary ideals of a -semigroup have been introduced and studied. Various characterization theorems of -semigroups have been obtained by using the notions of generalized bi-ideals and fuzzy generalized bi-ideals. The concepts of ideals, prime ideals, semiprime ideals in -semigroups have been generalized in terms of Atanassov's intuitionistic fuzzy subsets. Also the notions of intuitionistic fuzzy ideal extension in a semigroup and a -semigroup have been introduced and studied them directly and via operator semigroups of a -semigroup. Various characterization theorems of semigroups have also been obtained in terms of intuitionistic fuzzy magnified translation and intuitionistic fuzzy points.