Fuzzy functions with LSE

Fuzzy Functions'' are proposed to be determined by the least squares estimation (LSE) technique for the development of fuzzy system models. These functions, Fuzzy Functions with LSE'' are proposed as alternate representation and reasoning schemas to the fuzzy rule base approaches. These "Fuzzy Functions'' can be more easily obtained and implemented by those who are not familiar with an in-depth knowledge of fuzzy theory. Working knowledge of a fuzzy clustering algorithm such as FCM or its variations would be sufficient to obtain membership values of input vectors. The membership values together with scalar input variables are then used by the LSE technique to determine "Fuzzy Functions'' for each cluster identified by FCM. These functions are different from "Fuzzy Rule Base'' approaches as well as "Fuzzy Regression'' approaches. Various transformations of the membership values are included as new variables in addition to original selected scalar input variables; and at times, a logistic transformation of non-scalar original selected input variables may also be included as a new variable. A comparison of "Fuzzy Functions-LSE'' with Ordinary Least Squares Estimation (OLSE)'' approach show that "Fuzzy Function-LSE'' provide better results in the order of 10% or better with respect to RMSE measure for both training and test cases of data sets. (C) 2008 Elsevier B.V. All rights reserved.