Quotients with respect to similarity relations
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Rough-fuzzy-neurocomputing based on rough mereological calculus of granules
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On Rough Set Logics Based on Similarity Relations
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Rough-fuzzy-neurocomputing based on rough mereological calculus of granules
International Journal of Hybrid Intelligent Systems - Hybrid Intelligence using rough sets
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On Classifying Mappings Induced by Granular Structures
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Mereological theories of concepts in granular computing
Transactions on computational science II
RSKT'06 Proceedings of the First international conference on Rough Sets and Knowledge Technology
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In this work, we would like to discuss rough inclusions defined in Rough Mereology - a paradigm for approximate reasoning introduced by Polkowski and Skowron [20] - as a basis for common models for rough as well as fuzzy set theories. We would like to adhere to the point of view that tolerance (or, similarity) is the leading motif common to both theories and in this area paths between the two lie. To this end, we demonstrate that rough inclusions (which represent a hierarchy of tolerance relations) induce rough set theoretic approximations as well as partitions and equivalence relations in the sense of fuzzy set theory. For completeness sake, we also discuss granulation mechanisms based on rough inclusions with applications to Rough-Neuro Computing and Computing with Words. These considerations are also carried out in specialized cases of Menger's as well as Lukasiewicz's rough inclusions introduced in the paper.