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Characterization of neighborhood operators for covering based rough sets, using duality and adjointness

Covering based Rough Sets are an important generalization of Rough Set Theory. Basically, they replace the partition generated from an equivalence relation by a covering. In this context many approximation operators can be defined [16, 26, 27, 28, 34]. In this paper we want to discover relationships among approximation operators defined from neighborhoods. We use the concepts of duality, adjointness and conjugacy to characterize the approximation operators. Moreover we establish an order relation for these approximation operators.