一种新的犹豫模糊粗糙近似算子的公理刻画

Axiomatic Characterization of New Hesitant Fuzzy Rough Approximation Operators

为了揭示犹豫模糊粗糙近似算子更深层次的本质特性,且更进一步研究犹豫模糊粗糙近似空间与犹豫模糊拓扑空间之间的关系,对犹豫模糊粗糙近似算子公理刻画问题的研究具有重要意义.在已有结果中,用来刻画犹豫模糊近似算子的公理集大都含有多条公理.由于近似算子公理化方法在研究粗糙集理论的数学结构中具有重要意义,寻找最小公理集成为公理化方法中的一个基本问题.针对上述问题,首次将公理集中的公理简化为一条,提出一种新的公理刻画形式.首先给出一般犹豫模糊粗糙近似算子的公理刻画,然后分别针对串行的、自反的、对称的、传递的和等价的犹豫模糊关系所生成的犹豫模糊粗糙近似算子公理化问题进行研究.最后证明了由犹豫模糊粗糙近似空间可以诱导出一个犹豫模糊拓扑空间.

In order to reveal the deeper essential characteristics of hesitant fuzzy rough approximation operators and further study the relationship between hesitant fuzzy rough approximation spaces and hesitant fuzzy topological spaces, it is of great significance to study the axiomatic characterizations of hesitant fuzzy rough approximation operators. In most of the existing results, the axioms used to describe hesitant fuzzy approximation operators contain multiple axioms. Since the axiomatic characterization of approximation operator is a key method in the research of the mathematical structure of rough set theory, it is a fundamental problem in axiomatic method to find the minimum set of abstract axioms. In view of the above problems, this paper focuses on the study of characterization by using single axiom. The number of axioms in the axiom set is simplified to unique axiom for the first time, and a new axiom description is proposed. First of all, the axiomatic characterizations of classical hesitant fuzzy rough approximation operators are given. Then, we study the problem of the axiomatization of hesitant fuzzy rough approximation operators generated by serial, reflexive, symmetric, transitive and equivalent hesitant fuzzy relations, respectively. Finally, it is proved that the hesitant fuzzy rough approximation space can induce a hesitant fuzzy topological space.