The aim of the paper is to introduce degrees of satisfiability as well as a graded form of the meaning of formulas and their sets in the approximation space framework.
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In this paper we focus upon a comparison of some generalized rough approximations of sets, where the classical indiscernibility relation is generalized to any binary reflexive relation. We aim at finding the best of several candidates for generalized rough approximation mappings, where both definability of sets by elementary granules of information as well as the issue of distinction among positive, negative, and border regions of a set are taken into account.
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