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Bridging gaps between several forms of granular computing

Didier Dubois 1 Henri Prade 1
1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
IRIT - Institut de recherche en informatique de Toulouse
Abstract : Two important ideas at the core of Zadeh’s seminal contributions to fuzzy logic and approximate reasoning are the notions of granulation and that of possibilistic uncertainty. In this paper, elaborating on the basis of some formal analogy, recently laid bare 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 formal 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.
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Didier Dubois, Henri Prade. Bridging gaps between several forms of granular computing. Granular Computing, 2016, vol. 1 (n° 2), pp. 115-126. ⟨10.1007/s41066-015-0008-8⟩. ⟨hal-01484956⟩



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