Fuzzy reasoning method in fuzzy rule-based systems with general and specific rules for function approximation

Abstract

Discusses linguistic modeling of nonlinear functions with many inputs by fuzzy rule-based systems. That is, our task is to describe a multi-input nonlinear function by fuzzy if-then rules with linguistic interpretation. For a two-dimensional problem (i.e., for a two-input nonlinear function), we usually write linguistic rules in a tabular form, which is often used in fuzzy control problems. While such a tabular form is easily understood by human users, it can not scale up to high-dimensional problems because the number of rules exponentially increases with the dimensionality of the input space. For linguistically describing a nonlinear function with many inputs, we use general linguistic rules together with specific linguistic rules in a single fuzzy rule-based system. In the paper, we first show that the use of a standard fuzzy reasoning method sometimes leads to counterintuitive results. Then we propose a new fuzzy reasoning method that takes into account the specificity of each linguistic rule.