A systematic method of adaptive fuzzy logic modeling, using an improved fuzzy c-means clustering algorithm for rule generation

Complex dynamical systems, which are difficult to be mathematically modeled, can be described by a fuzzy model. This paper attempts to improve and to address the problems concerning the systematic fuzzy-logic modeling, by introducing the following concepts: 1) an effective theoretical base method to identify the optimum fuzziness parameter (weighting exponent) m instead of the heuristic selection method mainly reported in the literature; 2) an additional criterion to choose the optimum number of clusters (rules) using fuzzy model output variation with number of clusters; 3) a generalized and parameterized reasoning mechanism constructed based on the weighted sum of the normalized defuzzified output value of each individual rule. Fuzzy model with this reasoning mechanism is suitable for online learning and real-time control applications; and 4) a gradient-descent based parameter adjustment to tune the parameters of reasoning mechanism instead of the existing heuristic parameter identification in the literature. The proposed systematic method of fuzzy modeling has the advantages of simplicity, flexibility, and high accuracy. The two example data, which have been widely used in the textbooks and literature as benchmark, are used to evaluate the performance of the proposed method