Abstract
Ouyang et al. (Inf Sci 180:532–542, 2010) introduced the concept of (I, J)-fuzzy rough sets based on a pair of implications. Considering axiomatic characterization of approximation operators play a significant role in rough set theory, this paper devotes mainly to characterizing (I, J)-fuzzy rough sets based on a pair of implications from both constructive and axiomatic approaches. We firstly investigate the relationship between the lower and upper approximation operators based on a pair of ordinary implications and special fuzzy relations. And then (I, J)-fuzzy rough operators based on some special fuzzy relations are characterized by single axioms, which ensure the existence of polytypic fuzzy relations generating the same (I, J)-fuzzy rough approximation operators.
Published Version
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