| In this paper, the definitions of bipolar-value fuzzy soft ideals of semigroups,bipolar-value fuzzy soft interior ideals of semigroups,soft substructures of soft semigroups,soft (left,right) ideals were given and some of their related properties and equivalent conditions werediscussed.In addition,some properties of direct products of intuitionistic fuzzy completelyregular subsemigroups were investigated.This paper is organized as follows：In Chapter two,thedefinition of bipolar-value fuzzy soft ideals of semigroups is givenand several related properties are discussed,we proves that the intersection,“and”and unionunder the certain condition of two bipolar-value fuzzy soft ideals is also a bipolar-value fuzzysoft ideal.Furthermore, the properties of isomomorphic image and homomorphic pre-image ofbipolar-value fuzzy soft ideals of semigroups are investigated.In Chapter three,thedefinition of bipolar-value fuzzy soft interior ideals of semigroupsis given.And the paper proves that the intersection,“and”and union under the certaincondition of two bipolar-value fuzzy soft interior ideals is also a bipolar-value fuzzy softideal.On the basis of the Chapter two,the properties of isomomorphic image andhomomorphic pre-image of bipolar-value fuzzy soft interior ideals of semigroups arediscussed.In Chaper four,soft substructures of soft semigroups is investigated and the notions ofsoft subsemigroups, soft (left,right) ideals and soft homomorphisms of semigroups aregiven.The definition of soft homomorphism is introduced and related algebraic properties areobtained.In Chaper five,we discuss some properties of direct products of intuitionistic fuzzycompletely regular subsemigroups,and the equivalent characterizations are given by theconcept of level sets and cut sets on intuitionistic fuzzy sets.Based on the extensionprinciples,we investigate properties of image and the preimage of direct products ofintuitionistic fuzzy completely regular subsemigroups. |
PDF Full Text Request