Geveral Study Of Fuzzy Algebra

In this paper, the definitions of intuitionistic fuzzy strong regular subring,intuitionisticfuzzy completely regular subsemigroups, intuitionistic fuzzy soft subsemigroups ofcompletely regular semigroups, bipolar-value fuzzy soft subsemigroups of completely regularsemigroups, bipolar-value fuzzy soft bi-ideals of semigroups, Ω fuzzy interior ideals ofsemigroups, generalized Ω fuzzy interior ideals of semigroups, generalized Ω fuzzybi-ideals of semigroups were given. And some of their related properties and equivalentconditions were discussed. This paper is organized as follows：In Chapter three, the definitions of intuitionistic fuzzy strong regular subring is given,and some of its basic algebraic properties were discussed. The result that intersection of twointuitionistic fuzzy strong regular subring is also an intuitionistic fuzzy strong regular subringis obtained, by using the concept of cut sets on intuitionistic fuzzy sets, the equivalentcharacterizations of intuitionistic fuzzy strong regular subring are given.In Chapter four, we apply the concept of intuitionistic fuzzy soft sets to completelyregular semigroups.The new notion of intuitionistic fuzzy soft subsemigroups in completelyregular semigroups is introduced,and several related properties and equivalent characteri-zations are investgated.Finally,we discuss the properties of homomorphism image and prei-mage of intuitionistic fuzzy completely regular soft subsemigroup.In Chapter five, the notions of bipolar-value fuzzy soft subsemigroups of completelyregular semigroups are given, several basic properties are discussed.Finally,the definetionof bipolar-value fuzzy soft homomorphism and bipolar-value fuzzy soft isomomorphism ofcompletely regular semigroups are introduced and the properties of homomorphic preimageand isomomorphic image of bipolar-value fuzzy soft subsemigroups of completely regularsemigroups are investgated.In Chapter six, the notion of bipolar-value fuzzy soft bi-ideals of semigroups is given,and the property of “and”and”or” is investgated.The Necessary and sufficient conditionthat (f, A) is bipolar-value fuzzy soft bi-ideals of S is obtained.In Chapter seven, Given a set Ω,the notion of Ω fuzzy interior ideals of semigroupsis introduced,and Several basic properties and equivalent characterizations are discussed.Theproperties of homomorphism image and pre-image of Ω fuzzy interior ideals in semigroupsare investigated.Furthermore, by defining the multiply operation in SΩwe obtain thesemigroup (SΩ,),and investigate the interior ideals and Ω fuzzy interior ideals of SΩ.In Chapter eight, the notion of generalized Ω fuzzy interior ideals of semigroups isintroduced,and several related algebraic properties are discussed. Furthermore, by defining themultiply operation in SΩ, we obtain the semigroup (SΩ,),and investigate the interior ideals and generalized Ω fuzzy interior ideals of SΩ.In Chapter nine,the notion of generalized Ω fuzzy bi-ideals of semigroups isintroduced,and several related properties and equivalent characterizations are discussed. bydefining the multiply operation in SΩwe obtain the semigroup (SΩ,),and investigate thebi-ideals and generalized Ω fuzzy bi-ideals of SΩ.