(∈,∈∨q_λ,μ)-Fuzzy Inclines And Soft Inclines

Since Zadeh introduced the concept of fuzzy sets in 1965, many scholars have made a lot of researches on fuzzy algebra, which enriched the results of fuzzy algebra. Based on this, generalized fuzzy subinclines (ideals), (∈,∈∨q_(λ,μ))- fuzzy subinclines (ideals), generalized fuzzy subinclines (ideals) with norm T, generalized anti-fuzzy subinclines (ideals) and soft inclines are studied and discussed in this paper.Molodtsov gave the concept of soft sets in 1999, a new way of modeling vagueness and uncertainty. By appling the theories of soft sets to inclines, the definitions of soft inclines are given and discussed. Besides, the relations between soft inclines and fuzzy subinclines, (∈,∈∨q_(λ,μ))- fuzzy subinclines are studied.In the second chapter, preliminaries of this paper are given.In the third chapter, the concepts of generalized fuzzy subinclines (ideals) are given first in this paper. Then we discuss some related properties and get their some equivalent characterizations. Besides, we discuss the homomorphic preimage, the homomorphic image and the product of generalized fuzzy subinclines (ideals). Some meaningful results about them are obtained. Next the definitions of generalized fuzzy characteristic subinclines (ideals) are introduced. Subsequently, the equivalent characterizations are given. In the end, we introduce the notions of (∈,∈∨q_(λ,μ))- fuzzy subinclines(ideals) , do some researches into them and obtain that (∈,∈∨q_(λ,μ))- fuzzy subinclines(ideals) are equivalent to generalized fuzzy subinclines(ideals) .In the fourth chapter, the concepts of generalized fuzzy subinclines (ideals) with norm T are given . Then some of their properties are discussed. Based on this, their equivalent characterizations are also obtained .In the fifth chapter, the concepts of anti-fuzzy subinclines (ideals) and generalized anti-fuzzy subinclines (ideals) are given and some related properties are discussed in this paper. By using the definition of strong generalized order reversing, we obtain some meaningful results in generalized fuzzy subinclines and generalized anti-fuzzy subinclines. In the sixth chapter, the concepts of soft inclines, soft subinclines , soft ideals of soft inclines, and idealistic soft inclines are given and some related algebraic properties are discussed. The relations between soft inclines and several kinds of fuzzy subinclines are preliminarily investigated.