Axiomatic Characterizations of Reflexive and T-Transitive I-Intuitionistic Fuzzy Rough Approximation Operators

摘要

Axiomatic characterizations of approximation operators are important in the study of rough set theory. In this paper, axiomatic characterizations of relation-based intuitionistic fuzzy rough approximation operators determined by an intuitionistic fuzzy implication operator I are investigated. We present a set of axioms of lower/upper I-intuitionistic fuzzy set-theoretic operator which is necessary and sufficient for the existence of an intuitionistic fuzzy relation producing the same operator. We show that the lower and upper I-intuitionistic fuzzy rough approximation operators generated by an arbitrary intuitionistic fuzzy relation can be described by single axioms. Moreover, the J-intuitionistic fuzzy rough approximation operators generated by reflexive and T-transitive intuitionistic fuzzy relations can also be characterized by single axioms.