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On possibility theory, formal concepts analysis and granulation. (English) Zbl 1213.68620

Summary: 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 short paper, elaborating a bit on the basis of some mathematical analogy, recently made by the authors, between possibility theory and formal concept analysis, we suggest another bridge between the notion of extensional fuzzy set with respect to a similarity relation, and formal concept analysis. Thus, we point out some fruitful interactions between the possibilistic representation of information and two 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.

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
03E72 Theory of fuzzy sets, etc.
06A15 Galois correspondences, closure operators (in relation to ordered sets)
68T30 Knowledge representation
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
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