The Properties Of Fuzzy Soft Filter On Dual Soft Slope Algebra, Interval Soft Slope Algebra And FI Algebra

To solve problems of classical sets and uncertainty sets, the concept of soft sets was introduced by the Russian scholar Molodtsov in 1999. Many researchers attached great importance to soft sets theory because of its rich potential for appli-cations in several directions. In just ten years, a large number of related new ideas and of soft sets have emerged, and many scholars have applied it to daily life, the decision analysis, fuzzy soft sets, interval-valued fuzzy sets and fuzzy soft groups. Cai Xiaobo put forward the concept of dual soft sets and their properties were stud-ied. The first part of this paper further studied the properties of the dual soft sets on this basis. Moreover, the combination of soft sets-. interval soft sets and Incline algebras obtained some related conclusions.In the most study of logic algebras, the filters were the object of many research scholars. The second part of this article combined FI algebras and soft theory, and some properties of fuzzy soft filters are studied. Moreover, notions of fuzzy soft homomorphism and fuzzy soft isomorphism of fuzzy soft filters in FI algebras are given. At last, the theorems of isomorphism image and homomorphism pre-image of fuzzy soft filters in FI algebras are proven.The arrangement of this paper is as follows:Chapter one:Preliminaries. In this chapter, we introduces the preliminary concepts and results of the theory of soft sets, Incline algebra and FI algebras which will be used in the whole paper.Chapter two:Dual of soft Incline algebrals and interval soft Incline algebras. Firstly, with the help of the concept of the dual of soft sets, some primary properties of the dual of soft sets were studied; Secondly, the definition of the dual of soft Incline algebrals and some properties were studied, and particularly, properties of the dual of soft ideals and soft filters were studied. The definitions of homomorphism and isomorphism of the dual of soft Incline algebrals are introduced. Meanwhile, it was proven that the dual of soft Incline algebrals maintain the relationship of isomorphism under some circumstances. At last, the concept of interval soft sets was applied to Incline algebras. The notions of internal soft Incline algebras, internal soft Incline subalgebras and soft homomorphism between interval soft Incline algebras were defined and some basic properties were discussed. Some results of soft Incline algebras in related reference were generalized.Chapter three:Fuzzy soft filters in FI algebras. The definition of fuzzy soft filters and its equivalent description were introduced in FI algebras on the basic of FI algebras and soft sets theory. At last, some properties of fuzzy soft filters were studied. Moreover, theorems of isomorphism image and homomorphism pre-image of fuzzy soft filters in FI algebras were proven.