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

Abstract : 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.
Complete list of metadatas

Cited literature [41 references]  Display  Hide  Download
Contributor : Open Archive Toulouse Archive Ouverte (oatao) <>
Submitted on : Wednesday, March 8, 2017 - 10:08:05 AM
Last modification on : Thursday, October 17, 2019 - 8:54:11 AM
Long-term archiving on : Friday, June 9, 2017 - 12:40:07 PM


Files produced by the author(s)



Davide Ciucci, Didier Dubois, Henri Prade. Structures of opposition induced by relations - The Boolean and the gradual cases.. Annals of Mathematics and Artificial Intelligence, Springer Verlag, 2015, vol. 76 (n° 3), pp. 351-373. ⟨10.1007/s10472-015-9480-8⟩. ⟨hal-01485022⟩



Record views


Files downloads