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Structures of opposition induced by relations - The Boolean and the gradual cases.

Ciucci, Davide and Dubois, Didier and Prade, Henri Structures of opposition induced by relations - The Boolean and the gradual cases. (2015) Annals of Mathematics and Artificial Intelligence, 76 (3). 351-373. ISSN 1012-2443

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Official URL: http://dx.doi.org/10.1007/s10472-015-9480-8


The paper shows that a cube of opposition, a structure that generalizes the square of opposition invented in ancient logic, can be generated from the composition of a binary relation with a subset, by the effect of set complementation on the subset, on the relation, or on the result of the composition. Since the composition of relations is encountered in many areas, the structure of opposition exhibited by the cube of opposition has a universal flavor. In particular, it applies to information processing-oriented settings such as rough set theory, possibility theory, or formal concept analysis. We then discuss how this structure extends to a fuzzy relation and a fuzzy subset, and the graded cube of opposition thus obtained provides an organized view of the different existing compositions of fuzzy relations. The paper concludes by pointing out areas of research where the cube of opposition, or its graded version are of interest.

Item Type:Article
Additional Information:Thanks to Springer editor. The definitive version is available at http://link.springer.com The original PDF of this chapter can be found at: http://link.springer.com/article/10.1007/s10472-015-9480-8
HAL Id:hal-01485022
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Università degli Studi di Milano-Bicocca - BICOCCA (ITALY)
Laboratory name:
Deposited On:24 Feb 2017 13:47

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