Type 1 and Full Type 2 Fuzzy System Models

Abstract

We first present a brief review of the essentials fuzzy system models: Namely (1) Zadeh's rulebase model, (2) Takagi and Sugeno's model which is partly a rule base and partly a regression function and (3) Turksen fuzzy regression functions where a fuzzy regression function correspond to each fuzzy rule. Next we review the well known FCM algorithm which lets one to extract Type 1 membership values from a given data set for the development of Type 1 fuzzy system models as a foundation for the development of Full Type 2 fuzzy system models. For this purpose, we provide an algorithm which lets one to generate Full Type 2 membership value distributions for a development of second order fuzzy system models with our proposed second order data analysis. If required one can generate Full Type 3, ..., Full Type n fuzzy system models with an iterative execution of our algorithm. We present our application results graphically for TD_Stockprice data with respect to two validity indeces, namely: (1) elikyilmaz-Trksen and (2) Bezdek indeces.