Weighted fuzzy production rule reasoning with interactive propositions

Weighted fuzzy production rule reasoning is a kind of similarity-based reasoning. One frequently used model for weighted fuzzy production rule reasoning is to consider the weighted average of proposition-similarities as an overall similarity. Due to some inherent interaction among diverse propositions, the weighted average model does not work well in many real-world problems. The main purpose of the paper is to handle this kind of interaction by introducing a nonlinear integral tool in fuzzy production rule reasoning. Several non-linear integrals with respect to a fuzzy measure or a non-additive set function are outlined. The interaction among the propositions is considered to be reflected in the non-additive set function, and the overall similarity is computed by using the integral model instead of using the weighted average model. Because the weighted average can be regarded as a special case of nonlinear integral, the paper to some extent generalizes the application scope of similarity-based reasoning. Illustrative examples show that the inclusion of an expert measure enhances the representative and interpretive power of fuzzy production rules. In particular, while interaction exists among the propositions, the inclusion of an expert measure can reduce the likely occurrence of undesirable consequent