A Systematic Approach to Linguistic Fuzzy Modeling Based on Input - Output Data

A new systematic algorithm to build adaptive linguistic fuzzy models directly from input-output data is presented in this paper. Based on clustering and projection in the input and output spaces, significant inputs are selected, the number of clusters is determined, rules are generated automatically, and a linguistic fuzzy model is constructed. Then, using a simplified fuzzy reasoning mechanism, the Back-Propagation (BP) and Least Mean Squared (LMS) algorithms are implemented to tune the parameters of the membership functions. Compared to other algorithms, the new algorithm is both computationally and conceptually simple. The new algorithm is called the Linguistic Fuzzy Inference (LFI) model. 1 INTRODUCTION Fuzzy logic modeling techniques can be classified into three categories, namely the linguistic (Mamdani-type), the relational equation, and the Takagi, Sugeno and Kang (TSK). In linguistic models, both the antecedent and the consequence are fuzzy sets while in the TSK model the antecedent consists of fuzzy sets but the consequence is made up of linear equations. Fuzzy relational equation models aim at building the fuzzy relation matrices according to the input-output process data. Based on the TSK model, an Adaptive Network based Fuzzy Inference System (ANFIS) has been introduced by Jang (Jang 1993). This model is mostly suited to the modeling of nonlinear systems. It combines the recursive 48 least-square estimation and the steepest descent algorithms for calibrating both premise and consequent parameters iteratively. This algorithm is limited in incorporating human knowledge. In contrast, Linguistic fuzzy models are effective in embedding the human knowledge and have simpler forms. Systematic approaches to building linguistic fuzzy models are proposed in (Emami 1998, Sugeno. 1993). These approaches, however, involve nonlinear programming and are computationally cumbersome. This paper addresses this problem and proposes a new systematic and simple algorithm to build and tune models directly from the input-output data. Like ANFIS (Jang 1993) the new algorithm takes advantage of Neural Networks training techniques and it uses projection methods (Emami 1998, Sugeno 1993) to build the fuzzy rules. The new algorithm consists of two procedures. The first one is for fuzzy structure identification, in which the inputs, membership functions and fuzzy rules are determined. The second one is for fuzzy parameter identification, in which training algorithms are used to tune the parameters of the membership functions. 2 GENERAL LINGUISTIC FUZZY MODEL The general Linguistic Fuzzy Model of a Multi-Input Single-Output (MISO) system is interpreted by rules with multi-antecedent and single-consequent variables such as the following: Rule l: IF U1 is Bl1 AND U2 is Bl2 AND Ur is Blr THEN V is Dl , l = 1,2,…,n (1)