A systematic approach to fuzzy modeling for rule generation from numerical data

This paper addresses a new method for automatically extraction of the fuzzy rules from input-output data. The proposed fuzzy system modeling approach has three significant modules: (1) input selection; (2) knowledge representation; and (3) approximate reasoning. In the first module, a heuristic method is presented to select more significant input variables among the possible candidates. We decrease the number of inputs one by one with the improvement of a given criterion by implementing a neural network. In the second module, the data set is partitioned into several clusters according to their similarities. In this phase, we generalize Kwon index by using covariance norm matrix and implement the Gustafson-Kessel (GK) fuzzy clustering algorithm. Then, the results of fuzzy clusters are used for generation of fuzzy if-then rules, and neural networks optimize the membership functions of corresponding rules. The third module is parameterized inference formulation and optimization by implementing "sequential quadratic programming" algorithm. In this framework, the whole procedure of structure identification and parameter optimization is carried out automatically and efficiently by the combined use of neural networks, fuzzy clustering, and adaptive back-propagation learning. Finally, the proposed fuzzy methodology is implemented in supply chain of an automotive plant. The results show the superiority of the model in comparison with the Sugeno and Yasukawa\´s fuzzy modeling in terms of error reduction.