A review of several Fuzzy Function structures Abstract for NAFIPS 2009
Ismail Burhan Turksen · 2009
Within the last decade or so, there have been several proposals to develop fuzzy system models via functional representation in place of rule base representation. We review at least three of these approaches: 1) “Fuzzy Functions” originally proposed by Turksen I and later further developed by Celikyilmaz and Turksen I-I in a variety of versions. “Fuzzy Functions” are developed essentially with original input variables and membership values and their various transformations as required for a particular system representation. For this purpose membership values are obtained from FCM, Fuzzy C-Means I, or IFCM, Improved FCM, I algorithm. Thus, this approach requires the availability of an input-output data base for analysis by FCM or IFCM algorithm for the extraction of membership values. There is a “Fuzzy Functions” for each cluster. Thus, “Fuzzy Functions” are an improved alternate system models to “Fuzzy Rule Bases”. 2) The objective of “Fuzzy C-Regression Model”, (FCRM), clustering algorithm I, as in all clustering algorithms, is to classify objects into similar groups. FCRM clustering algorithm yields simultaneous estimates of parameters of “C-Regression Models”, while fuzzy partitioning a given dataset. A prominent feature of this clustering algorithm that separates it from other point-wise clustering algorithms, e.g. FCM, is that, cluster prototypes are functions instead of geometrical objects. 3) Höppner and Klawonn I combine FCM I, and FCRM I algorithms in one clustering schema, to build a combined clustering structure. Their main goal was to update FCM fuzzy clustering algorithm so that they can prevent the effect of harmonics by modifying the objective function. They not only deal with point-wise clustering algorithms such as “Fuzzy C-Means” (FCM) clustering algorithm I, they also deal with “Fuzzy C-Regression Model” clustering algorithm (FCRM) I. It is also well-known that Hathaway and Bezdek, 1993, proposed to build linear regression models. Whereas one can build non-linear regression models with Höppner and Klawonn, 2003, approach