Abstract
Different from rough sets in Pawlak’s sense, which is a binary approximation operations based structure, in this paper, we propose a new rough equivalence relation based on triple approximation operations induced by selection function. The same as traditional rough sets research, we consider the algebra issue of new rough sets system and construct lattice structure in an algebraic fashion. An isomorphic relationship is studied between proposed rough sets algebra structure and that in Pawlak’s sense. In addition, some examples are shown and studied in order to indicate the effectiveness of new equivalence relation in distinguishing and describing subsets of universe. Besides, we also study restriction of selection congruence on subalgebra built by covering of universe. Finally, conclusion on the axioms of middle approximation operation are shown to clarify properties of new structure.
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