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Using One Axiom to Characterize Fuzzy Rough Approximation Operators Determined by a Fuzzy Implication Operator

Wu W.-Z., Li T-J., Gu S.-M.

Fundamenta Informaticae

2015

Vol. 142, nr 1-4

87--104

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.