Singular value-based approximation with Takagi-Sugeno type fuzzy rule base

In order to design a fuzzy rule base two important aims have to be taken into consideration: 1) to achieve a good approximation, and 2) to reduce the number of rules. A main difficulty in fuzzy applications, however, is that these two aims are contradictory. This paper introduces a new approach of Takagi-Sugeno type fuzzy approximation. The new method filters out the irrelevant information in the rule base to reduce the number of antecedent sets, hence the number of rules. This proposed method is a nonlinear extension of the recently published fuzzy approximation approach based on singular value decomposition which utilizes singleton support. The approximation error bound of reduced rule base, the extension to general number of variables and the use of various kind of Takagi-Sugeno functions are discussed. An example is included to illustrate the effectiveness of the proposed method.