Fuzzy arithmetic-based interpolative reasoning

Fuzzy Arithmetic based Interpolative Reasoning is presented. Linguistic rules of the Mamdani type with fuzzy numbers as consequents are used in an inference mechanism similar to that of the Takagi-Sugeno model. The inference result is a weighted sum of fuzzy numbers calculated by means of the extension principle. Both fuzzy and crisp inputs and outputs can be used, and chaining of rule bases is supported without increasing the fuzziness in each step. This provides a setting for the modeling of dynamic fuzzy systems by fuzzy recursion. The matching in the rule antecedents is done by means of a compatibility measure. Different compatibility measures can be used for different antecedent variables, and reasoning with sparse rule bases is supported. Application of FAIR to the modeling of a nonlinear dynamic system is presented as an example. Copyright (C) 1998 IFAC.