Rough mereology as a link between rough and fuzzy set theories. A survey

Abstract

In this paper, we discuss rough inclusions defined in Rough Mereology - a paradigm for approximate reasoning introduced by Polkowski and Skowron - as a basis for common models for rough as well as fuzzy set theories. We justify the point of view that tolerance (or, similarity) is the motif common to both theories. To this end, we demonstrate in Sect. 6 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. Before that, we include an account of mereological theory in Sect. 3. We also discuss granulation mechanisms based on rough inclusions with an outline of applications to rough-fuzzy-neurocomputing and computing with words in Sects. 4 and 5. © Springer-Verlag 2004.