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.
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