【作者】 段瑞霞；

【导师】 袁学海；

【作者基本信息】 辽宁师范大学 ， 应用数学， 2007， 硕士

【摘要】 首先，利用模糊点与模糊集合的邻属关系，引入了(α，β)-模糊等价关系和((?)，(?))-模糊等价关系的概念，并探讨了当α，β分别为∈，q，∈(?)q，∈(?)q的情况下，((?)，(?))-模糊等价关系的性质。由此我们得到((?)，(?))-模糊等价关系中有意义的是(∈，∈)-模糊等价关系，(∈，∈(?)q)-模糊等价关系和((?)，(?))-模糊等价关系。其次，给出了(λ，μ]-模糊等价关系的定义，并研究了(λ，μ]-模糊等价关系与经典等价关系的关系。最后，引入了一种新的模糊集截集(λ，μ]-α-截集，并对这种截集的性质进行了讨论。同时根据表现定理，引入了模糊集的(λ，μ]-粗糙集的概念，并研究了模糊集的(λ，μ]-粗糙集与模糊集之间的关系。在此基础上，通过构造性的方法，给出了当R是论域X上的一个(λ，μ]-模糊等价关系时，近似空间(X，R)上的模糊粗糙集模型，并对它们的性质进行了讨论。更多还原

【Abstract】 Content: First, by the use of the relation between fuzzy points and fuzzysets, the definitions of (α,β)-fuzzy relation of equivalence and(β,α)-fuzzy relation of equivalence are introduced. Some properties of(β,α)-fuzzy relation of equivalence are obtained, whereα,βdenoteany one of∈, q,∈∨q,∈∧q. It has been found that acceptable non-trivialconcepts obtained in this manner are (∈,∈)-fuzzy relation of equivalence,(∈,∈∨q)-fuzzy relation of equivalence and ((?), (?)∨(?))-fuzzy relation ofequivalence.Second, the definition of (λ,μ]-fuzzy relation of equivalence isintroduced. The relation between (λ,μ]-fuzzy relation of equivalenceand classical relation of equivalence are discussed.Finally, a new kind of cut sets is introduced and some properties oftheses cut sets are presented. Based on representation theorem, theconcept of (λ,μ]-rough set is introduced and the relation between(λ,μ]-rough set and fuzzy set are discussed. By the constructive method,when R is a (λ,μ]-fuzzy relation of equivalence, fuzzy rough setmodels in the approximate space (X, R)are obtained and someproperties of them are presented.更多还原