Approximation of the smooth functions by using fuzzy systems = A review of the advantages

다국어 초록 (Multilingual Abstract)

A review of how the functions of two or more independent variables can be approximated by using fuzzy systems is provided in this paper. We start with an exact represention of a linear interpolation function of two independent variables by using a fuzzy system. Next, we describe how this function can be approximated by another fuzzy system wi th a lesser number or wi th a desired number of output fuzzy sets. Thus, a reduction of the storage needed is achieved by storing the fuzzy rules or equivalently the output fuzzy set numbers instead of storing the whole discrete function values. A description on how the cubic spline interpolation function can be represented exactly by using the fuzzy system method is provided, along with a few examples where fuzzy rule tables with a size of 7×7 provide a representation of the functions with relative errors of the order of 10<SUP>-2</SUP> or less.

목차 (Table of Contents)

• Abstract
• 1. Introduction
• 2. A fuzzy system to represent linear interpolation functions
• 3. A fuzzy system to represent the cubic spline interpolation function
• 4. Examples
• 5. Conclusion
• 6. References