A Novel Multiplicative Fuzzy Regression Function with A Multiplicative Fuzzy Clustering Algorithm

Possible structures of the system which is composed of various input and output variables are described by Fuzzy System Modeling(FSM). Traditional FSM approaches such as fuzzy rule-based systems and fuzzy regression functions have high ability to ensure approximating the real-world systems. Fuzzy Functions with Least squares Estimation(FF-LSE) is proposed by Turksen [1] for development of fuzzy system models. In the FF-LSE method, Improved Fuzzy Clustering(IFC) is used to find membership values in regression and classification type datasets, separately. In this study, we propose a novel FSM approach, namely Multiplicative Fuzzy Regression Function(MFRF), which is constructed based on a new Multiplicative Fuzzy Clustering(MFC) algorithm. In the MFC algorithm, membership values are initially computed by Fuzzy c-Means Clustering(FCM) algorithm, then additional transformations of the membership values are used to generate multiplicative fuzzy functions(MFFs) for each cluster. The additional transformations of the membership values together with input variables are used by the Least Squares Estimation to form Multiplicative Fuzzy Regression Functions for each cluster identified by Multiplicative Fuzzy Clustering. Computational complexity of the proposed MFRF method is discussed and its performance is examined using several experiments on Concrete Compressive Strength dataset. Performance of the proposed MFRF is compared to FF-LSE and classical LSE approaches.