Axiomatic characterizations of (S, T)-fuzzy rough approximation operators

作者：Wu, Wei-Zhi^*; Xu, You-Hong; Shao, Ming-Wen; Wang, Guoyin

来源：Information Sciences, 2016, 334: 17-43.

DOI：10.1016/j.ins.2015.11.028

• Approximation operators
• Fuzzy relations
• Fuzzy rough sets
• Rough sets
• Triangular norms

Axiomatic characterizations of approximation operators are of importance in the study of rough set theory. In this paper axiomatic characterizations of relation-based (S, T)-fuzzy rough approximation operators are investigated. By employing a triangular conorm S and a triangular norm T on [0, 1], we first introduced the constructive definitions of S-lower and T-upper fuzzy rough approximation operators with their essential properties. We then propose an operator-oriented characterization of (S, T)-fuzzy rough sets, that is, fuzzy set-theoretic operators defined by axioms guarantee the existence of different types of fuzzy relations which produce the same operators. We show that the S-lower (and, respectively, T-upper) fuzzy rough approximation operators generated by a generalized fuzzy relation can be described by only one axiom. We further show that (S, T)-fuzzy rough approximation operators corresponding to special types of fuzzy relations, such as serial, reflexive, symmetric, and T-transitive ones as well as any of their compositions, can also be characterized by single axioms.

• 出版日期2016-3-20
• 单位中国石油大学（北京）; 重庆邮电大学; 浙江海洋大学