ISSN 1000-1239 CN 11-1777/TP

### Axiomatic Characterization of New Hesitant Fuzzy Rough Approximation Operators

Liu Wen1, Mi Jusheng1, Sun Yan2

1. 1School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024）

2School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081）

• Supported by:
This work was supported by the National Natural Science Foundation of China (62076088, 61502144), the Natural Science Foundation of Hebei Province (F2018205196, F2019205295), the Natural Science Foundation of Higher Education Institutions of Hebei Province (BJ2019014), the Postdoctoral Advanced Programs of Hebei Province (B2016003013), and the Training Funds for 333 Talents Project in Hebei Province (A2017002112).

Abstract: 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.