A Comparison of Fuzzy Functions with LSE and TS-Fuzzy Methods in Modeling Uncertain Datasets

Abstract

This paper compares the success of approximation of two fuzzy modeling methods: Takagi-Sugeno's Fuzzy Model (TS) against the Turksen's Fuzzy Function with Least Squares Estimation (FF-LSE) using five highly uncertain benchmark datasets. TS modeling can be considered as a local linear approximation of a data set with multidimensional linear consequents in its fuzzy rulebase. TS Multidimensional reasoning is further extended by Turksen using multidimensional fuzzy sets at the antecedent part of the fuzzy rules. Compared to Ordinary Least Squares Estimation, the modeling error of FF-LSE was reported to be up to 10% less. Our tests with 5 benchmark data indicated that FF-LSE gives mostly less prediction error than TS model. Reduction of RMSE reaches up to 25%, and in average around 10%.