Bridging gaps between several frameworks for the idea of granulation

Abstract

Two important ideas at the core of Zadeh's seminal contributions to fuzzy logic and approximate reasoning are the notions of granulation and of possibilistic uncertainty. In this paper, elaborating on the basis of some formal analogy, recently made by the authors, between possibility theory and formal concept analysis, we suggest other bridges between theories for which the concept of granulation is central. We highlight the common features between the notion of extensional fuzzy set with respect to a similarity relation and the notion of concept. We also discuss the case of fuzzy rough sets. Thus, we point out some fruitful cross-fertilizations between the possibilistic representation of information and several views of granulation emphasizing the idea of clusters of points that can be identified respectively on the basis of their closeness, or of their common labeling in terms of properties.