Fuzzy Sets and Systems In ( 1983) 2 I l-222 North-Holland 211 ON MEDICAL DIAGNOSIS USING POSSIBILITY MEASURES M.A. VILA and M. DELGADO Depcwtctrner~rr~ de Estadkticn Maremcirica, Cemro de Informdtica. Universidad de Granada, Grarda. Spciirl Rcccivcd July I983 Rcvisrd Scptcmhcr 1 OS2 This paper prexnts a model of clinical diagnosis in the context of possibility distributions. By using B-optimal mcmbe&ip functions, an expression for automatic diagnosis is formulated for a concrctc fuzzy set of symptoms. Their properties and relation with the composition of fu7Ty relations arc analyzed hy means of a new formulation of fuzzy integrals for additive fuzzy measurch. A practical C:IW is also annlyzcd. Keywords: Medical tliagnoGs. Possibility distributions. Conditional possibility distribution, Fuzzy measures. Fuzzy integrals. Composition of fuzzy relati~ms. Bayes-optimal mcmhership functions. 1. Introduction Medical diagnosis, involving data and relations of fuzzy kind, has been dealt with by many authors, for instance Sanchez, Bezdeck etc. In this paper we propose an automatic diagnosis method based on possibility theory [3] and the properties of Sugeno’s integral for additive f-measures. We shall consider a model where a possibility distribution on the set X(symptoms) x Nldiseases), ~(x, i) is previously known. Then the problem is to find a possibility distribution on N, i.e. a diagnosis corresponding to a given fuzzy set of X which represents the symptoms of a concrete patient: in such a way that this reflects the previous relation ~(x, il. We propose a formulation for this distribution which is based on the B-optimal membership functions [7] induced by ~(x. i), and we shall analyze some proper- ties of this formulation using an expression of Sugeno’s fuzzy integral for additive fuzzy measures which are also proved in the paper. Finally a practical case of clinical diagnosis is studied comparing the real and automatic diagnosis. 2. The model. Notation and previous concepts Let finite sets X and N respectively stand for symptoms and diseases. Let us assume that a possibility distribution r(., .) on XX N is obtained by some 0160114/83/$03.00 0 1983 Elsevier Science Publishers B.V. (North-Holland)