Recent advances in fuzzy system modeling

Abstract

Decision making under uncertainty is an interdisciplinary research field.In this chapter, we attempt to create a framework for the human decision-making processes withType 1 and FullType 2 Fuzzy Logic methodology. For this purpose, we first present a brief review of the essentials of (1) Zadeh's rule basemodel,(2) Takagi and Sugeno's model which is partly a rule baseand partly a regression function, and (3) TÜrkşen's model of fuzzy regression functions where a fuzzy regressionfunction corresponds to each fuzzy rule in a fuzzy rule base model. Next, wereview the well-known fuzzy C-means (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 systemmodels.Forhispurpose, we provide an algorithm which lets one to generate Full Type 2 membership value distributions for a development of second-order fuzzy systemmodels 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 proposedalgorith.We present our applied results graphically for TD_Stockprice data with respect to two validity indices, namely (1) Çelikyılmaz-TÜrkşen and (2) Bezdek indices. © Springer Science+Business Media, LLC 2015.