UNIFIED STRUCTURE AND PARAMETER-IDENTIFICATION OF FUZZY MODELS

The unified approach to fuzzy modeling developed in this correspondence addresses the problems of structure and parameter identification of fuzzy models. It demonstrates an alternative view to structure identification, transforming the problem of structure identification to estimation of the distribution of input space. A new concept of sample probability distributions (SPD) is introduced and a family of SPD is constructed. This allows us to simplify the problem of structure identification by replacing identification of membership functions of input variables with identification of the centers of cluster-like regions. The fuzzy model complex of fuzzy model is also discussed in connection with the modeler's confidence and two types of confidence-a priori and a posteriori confidence-are also suggested. The identification problem is solved also under the additional requirement of simplification of the model structure. A learning algorithm realizing structure and parameter identification of QLFM with the simplest structure is proposed.