Mixed Fuzzy Functions

Abstract

Mixed-Fuzzy Functions are proposed as an alternate to Fuzzy Rule Base formation in the structure identification of system models and reasoning with them. These Mixed-Fuzzy Functions can be determined by any function identification method such as least squares' estimates, ILSE, maximum likelihood estimates, NME, support vector machines, SVM, etc. For this purpose, working knowledge of a fuzzy clustering algorithm such as FCM or its variations, such as Improved Fuzzy Clustering Method (IFCM), 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 "Mixed Fuzzy Functions" for each cluster identified by FCM and/IFCM. These functions are different from "Fuzzy Rule Base" approaches as well as "Fuzzy Regression" approaches. In Mixed Fuzzy Functions, 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.