(∈,∈∨q(λ,μ)-(Intuitionistic) Fuzzy Semirings

In this paper, the definitions of (e,e vq(Ap))-fuzzy complemented semirings, Q-fuzzy complemented subsemirings,(e,ev<7(/J/i))-fuzzy complemented semirings,(e,e v^Ua))â– fuzzy k-left(right) ideals of semirings, intuitionistic fuzzy complemented subsemirings were given. And some of their related properties and equivalent conditions were discussed.The main results obtained in this dissertation are summarized as follows:In Chapter three,the definitions of (e,evg(i))â– fuzzy complemented semirings and generalized fuzzy complemented semirings are first given.Then,some of the fundamental properties and some equivalent characterizations of such(e,e\/q{/ifl))-fuzzy complemented semirings are also discussed.Finally,we have obtained some properties of homomorphic image and homomorphic preimage of it by using the pointwise method.In Chapter four, the definition of (e,evg(/J^)-fuzzy complemented semirings is first given.Then,some of the fundamental properties and some equivalent characterizations of such (e,î–¼^(1/j|)-fuzzy complemented semirings are also discussed.Finally,we have obtained some relative results of homomorphic image and homomorphic preimage of it based on the anti-extension principle.In Chapter five,given a set Q,the notion of Q-fuzzy complemented subsimirings of complemented semiring is introduced,and some basic propeities are investigated.Several equivalent characterizations of Q-fuzzy complemented subsimirings are obtained.We prove that the intersection of two Q-fuzzy complemented subsemiring,the homomorphism image or homomorphism preimage of Q-fuzzy complemented subsemiring are also Q-fuzzy complemented subsemiring.Finally,by defining theâ– ,â– ,-operations in sn we obtain the complemented semiring (Sn,â– ,<8>,-),investigatethe relevant fuzzy complemented subsemiring and Q-fuzzy complemented subsemiring.In Chapter six,the concepts of (e,e vq[A/j))-fuzzy A:-left(right) ideals and generalized fuzzy kâ– left(right) ideals of semiring are given and some equivalent characterizations and some properties of (e, e vqu)â– fuzzy kâ– left(right) ideals of semiring are also obtained. Besides,we also disscuss some properties of homomorphicimage and homomorphic preimage of it.In Chapter seven,on the basis of the intuitionistic fuzzy sets being introduced by K.Atanassov, we define intuitionistic fuzzy complemented subsemirings, then we discuss its basic properties,the equivalent characterizations are given by the concept of cut sets on intuit-Tionistic fuzzy sets.Besides,in the sense of homomorphism and isomorphism of complement-ed subsemirings,we investigate image and the inverse image of intuitionistic fuzzy comple-mented subsemirings.