Abstract
The paper proposes a diagnostic method employing Possibility theory. There has been a way to solve the inverse problem of fuzzy relational equation as a diagnostic method using fuzzy causal relations between causes and symptoms. The causalities between fuzzy set A on possible causes U and B on possible symptoms V are given as a fuzzy relation R on U×V. Then, the diagnosis is to obtain A by solving a fuzzy relational equation B=A○R under the conditions of given R and B. In the diagnostic process, the membership values of fuzzy set B are interpreted as degrees or intensities of symptoms, while those of fuzzy set A are done as possibilities or certainties of causes. This interpretation, however, shows that different measures of fuzziness-intensity and possibility-are confusingly mixed in a equation. According to Possibility theory, fuzzy sets A, B and fuzzy relation R in a fuzzy relational equation could be understood as possibility distributions π_U(u_i), π_V(v_i)on U, V and a conditonal possibility distribution π_<V|U>(v_i|u_i)on U×V, respectively. Therefore, in this paper, we define diagnostic problem as a problem to obtain possibility that any crisp subset of U is the set of causes of a given crisp subset of V as symptoms, where possibility distribution π_U(u_i)on U and conditional possibility distribution π_<Y|U>(v_i|u_i)are given as a priori knowledge. Then, the way to solve the problem is discussed and proposed.
