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Approximation Spaces Based on Relations of Similarity and Dissimilarity of Objects

In this article, we aim at extension of similarity-based approximation spaces to the case, where both similarity and dissimilarity of objects are taken into account. Apart from the wellknown notions of lower rough approximation, upper rough approximation, and variable-precision positive regions of concepts, adapted to our case, the notions of exterior, possibly negative region, and ignorance region of concepts are introduced and investigated.