Estimation of Probability Parameters in Probabilistic Fuzzy Systems

The rule base of a Probabilistic Fuzzy System (PFS) consists of fuzzy rules that have multiple consequent parts. Each consequent has an associated probability parameter. This paper is concerned with the estimation of the probability parameters in a PFS. It is assumed in this paper that both the antecedent and the consequent membership functions (mfs) have already been determined and need not be further optimized. In this paper, we show that the conditional probability method generally does not give optimal results in terms of the approximation accuracy of a PFS. As an alternative, we propose to use the maximum likelihood (ML) criterion for estimating the probability parameters in a PFS.

Keywords:

Conditional Probability , Fuzzy Rules , Maximum Likelihood , Probabilistic Fuzzy System