Rough Mereology: A Rough Set Paradigm for Unifying Rough Set Theory and Fuzzy Set Theory

Article type: Research Article

Authors: Polkowski, Lech

Affiliations: Polish–Japanese Institute of Information Technology, Koszykowa 86, 02-008 Warsaw, Poland

Abstract: 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.

Keywords: rough set theory, fuzzy set theory, rough mereology, rough inclusions, granular calculus

Journal: Fundamenta Informaticae, vol. 54, no. 1, pp. 67-88, 2003