Quotients with respect to similarity relations
Fuzzy Sets and Systems - Mathematics and Fuzziness, Part 1
Advances in the Dempster-Shafer theory of evidence
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough-Neuro-Computing: Techniques for Computing with Words
Rough-Neuro-Computing: Techniques for Computing with Words
Rough Sets: Mathematical Foundations
Rough Sets: Mathematical Foundations
Similarity relations and fuzzy orderings
Information Sciences: an International Journal
Computing with Words in Information/Intelligent Systems 2: Applications
Computing with Words in Information/Intelligent Systems 2: Applications
Fundamenta Informaticae - New Frontiers in Scientific Discovery - Commemorating the Life and Work of Zdzislaw Pawlak
On Rough Set Logics Based on Similarity Relations
Fundamenta Informaticae - Contagious Creativity - In Honor of the 80th Birthday of Professor Solomon Marcus
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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 Łukasiewicz's rough inclusions introduced in the paper.