Fuzziness in a topos

Stéphane Puechmorel (1)

1 ENAC - Ecole Nationale de l'Aviation Civile

Elementary topos can be seen as a categorical axiomatization of the classical set theory. They are basically categories in which each subobject can be uniquely described by reference to a subobject (named "true") of a distinguished object, the subobject classifier. Morphisms from an object to the subobject classifier can then be seen as a membership morphism. Introducing fuzziness in a topos requires working not with points, which is a non-elementary notion, but with whole sets of subobjects. A comma construction with the category of *-autonomous lattices gives the desired category of fuzzy sets of subobjects.

Mots clés: fuzzy logic; fuzzy set theory

Domaines: Optimisation et contrôle [math.OC]

Stéphane Puechmorel. Fuzziness in a topos. WCCI 98, International Conference on Fuzzy Systems at the World Congress on Computational Intelligence, 4-9 May 1998, May 1998, Anchorage, United States. pp 841-844, ⟨10.1109/FUZZY.1998.687600⟩. ⟨hal-01020961⟩