Affiliations: [a] School of Mathematics, Physics and Information Science and Key Laboratory of Oceanographic Big Data Mining & Application of Zhejiang Province, Zhejiang Ocean University, Zhoushan, Zhejiang 316022, P. R. China. [email protected], [email protected], [email protected]
Correspondence:
[†]
Address for correspondence: School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang 316022, P. R. China.
Note: [*] This work was supported by grants from the National Natural Science Foundation of China (Nos. 61573321, 61272021, 61202206, and 61173181), and the Zhejiang Provincial Natural Science Foundation of China (Nos. LZ12F03002 and LY14F030001).
Abstract: Axiomatic characterizations of approximation operators are important in the study of rough set theory. In this paper, axiomatic characterizations of relation-based fuzzy rough approximation operators determined by a fuzzy implication operator ℐ are investigated. We first review the constructive definitions and properties of lower and upper ℐ-fuzzy rough approximation operators. We then propose an operator-oriented characterization of ℐ-fuzzy rough sets. We show that the lower and upper ℐ-fuzzy rough approximation operators generated by an arbitrary fuzzy relation can be described by single axioms. We further examine that ℐ-fuzzy rough approximation operators corresponding to some special types of fuzzy relations, such as serial, reflexive, and 𝒯-transitive ones, can also be characterized by single axioms.
