Fuzzy relation equations and causal reasoning

Fuzzy relation-based models for handling uncertainty (in a non-probabilistic way) in diagnosis problems have been introduced by Sanchez about twenty years ago, and since then applied and developed by several researchers. The paper first reviews the existing proposals, also including the association-based abductive model proposed by Reggia and his co-workers, which uses non-fuzzy relations. A new model is presented in order to have a more expressive representation capable of handling uncertainty, and also of distinguishing, i) between manifestations which are certainly absent from those which are not (yet) observed, and ii) between manifestations which cannot be caused by a given disorder and manifestations for which we do not know if they can or cannot be caused by this disorder. This new model is based on possibility theory and the so-called twofold fuzzy sets, previously introduced by the authors.