Fuzzy Sets and Systems 137 (2003) 177–188 www.elsevier.com/locate/fss Abductive reasoning and measures of similitude in the presence of fuzzy rules N edra Mellouli ∗ , Bernadette Bouchon-Meunier Universit e Pierre et Marie Curie, LIP6, 8, rue du capitaine Scott, 75015 Paris, France Abstract In decision-making problems, several methods exist in the literature. This paper shows how abductive reasoning can be a useful approach to deal with incomplete information. Our contribution proposes a model based on fuzzy gradual rules and fuzzy observations and operating in two steps. In the rst step, we construct abductive hypotheses by using an inference method based on mathematical properties of generalized modus ponens. These hypotheses are not uniquely dened. This is why in the second step, we dene two types of criteria to construct the best ones according to the given observation. These criteria are, respectively, the similitude and the coherence, which we propose to study in detail in this paper. c  2002 Published by Elsevier Science B.V. 1. Introduction Decision making is a major problem in knowledge based systems. It becomes more and more dicult and delicate when knowledge is fuzzy. In this paper, we try to characterize the best decision in the framework of a rule-based system, on hypothesis driven reasoning. These hypotheses result from abductive reasoning on fuzzy rules. Abductive reasoning with rules is a suitable procedure to generate hypotheses from observations. 1 Let us illustrate our problem with the following simple example. We give two fuzzy rules: if the trac is crowded then the ow is low; if the visibility is weak then the ow is low; Moreover, we know that we must expect a trac jam when the trac is crowded and we must reduce the speed when the visibility is weak. Now, we suppose that we observe ‘the ow is very low’, according to these two linguistic rules and to the corresponding observation, we rst construct hypotheses by abduction such as the trac * Corresponding author. 1 In the context of our study, fuzzy observations match conclusions of rules. Hypotheses generated by abductive inference match premises of the rules. 0165-0114/03/$-see front matter c  2002 Published by Elsevier Science B.V. PII:S0165-0114(02)00439-6