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Graded cubes of opposition and possibility theory with fuzzy events

Dubois, Didier and Prade, Henri and Rico, Agnès Graded cubes of opposition and possibility theory with fuzzy events. (2017) International Journal of Approximate Reasoning, 84. 168-185. ISSN 0888-613X

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Official URL: https://doi.org/10.1016/j.ijar.2017.02.006


The paper discusses graded extensions of the cube of opposition, a structure that naturally emerges from the square of opposition in philosophical logic. These extensions of the cube of opposition agree with possibility theory and its four set functions. This extended cube then provides a synthetic and unified view of possibility theory. This is an opportunity to revisit basic notions of possibility theory, in particular regarding the handling of fuzzy events. It turns out that in possibility theory, two extensions of the four basic set functions to fuzzy events exist, which are needed for serving different purposes. The expressions of these extensions involve many-valued conjunction and implication operators that are related either via semi-duality or via residuation.

Item Type:Article
Additional Information:Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com The original PDF of the article can be found at : https://www.sciencedirect.com/science/article/pii/S0888613X17301391
HAL Id:hal-01919020
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 > Université Claude Bernard-Lyon I - UCBL (FRANCE)
Laboratory name:
Deposited On:18 Oct 2018 13:19

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