Rough set model based on axiomatic fuzzy set

Article type: Research Article

Authors: Xu, Siyu^{; *} | Qin, Keyun | Pan, Xiaodong | Fu, Chao

Affiliations: School of Mathematics, Southwest Jiaotong University, Chengdu, PR, China

Correspondence: [*] Corresponding author. Siyu Xu. E-mail: [email protected].

Abstract:  Both fuzzy set and rough set are important mathematical tools to describe incomplete and uncertain information, and they are highly complementary to each other. What is more, most fuzzy rough sets are obtained by combining Zadeh fuzzy sets and Pawlak rough sets. There are few reports about the combination of axiomatic fuzzy sets and Pawlak rough sets. For this reason, we propose the axiomatic fuzzy rough sets (namely rough set model with respect to the axiomatic fuzzy set) establishing on fuzzy membership space. In this paper, we first present a similarity description method based on vague partitions. Then the concept of similarity operator is proposed to describe uncertainty in the fuzzy approximation space. Finally, some characterizations concerning upper and lower approximation operators are shown, including basic properties. Furthermore, we give a algorithm to verify the effectiveness and efficiency of the model.

Keywords: Rough sets, axiomatic fuzzy rough sets, residuated lattices, fuzzy relations, approximation operators

DOI: 10.3233/JIFS-223643

Journal: Journal of Intelligent & Fuzzy Systems, vol. 45, no. 1, pp. 1423-1436, 2023