Identification of membership functions based on fuzzy observation data

For the classification problem, of which categories having vague or verbal definition, Okuda et al. [Proc. 3rd IFSA Congr. (1989) 755] proposed a model in which each category is defined by fuzzy sets, and each appearance frequency is explained by the probability of Zadeh's fuzzy event. They called this model fuzzy observation. Membership functions are usually given directly by the user's subjectivity. But these membership functions cannot be used in the fuzzy observation model because they have no assurance to meet the restriction as the fuzzy event. In this paper we propose a method to obtain the membership functions which satisfy the restriction as the fuzzy event against to given probability density function, and discuss the effectiveness of the method. (C) 1998 Elsevier Science B.V.