A logic of the similarity with prototypes and its relationship to fuzzy logic

Fuzzy sets are widely used to model vague properties. According to a common understanding, a fuzzy set represents the degrees of similarity of precisely specified objects with the prototypes of the considered vague property. We propose a logic based on this idea, using an entailment relation which was introduced in a work of Dubois, Prade, Esteva, Garcia, and Godo. The logic allows reasoning about the similarity with specific sets of prototypes; however, set-theoretic operations among the sets of prototypes associated to different properties are not dealt with. We arrive at a formalism closely related to fuzzy logic.