IDENTIFICATION OF FUZZY PREDICTION MODELS THROUGH HYPERELLIPSOIDAL CLUSTERING

To build a fuzzy model, as proposed by Takagi and Sugeno, we emphasize an interactive approach in which our knowledge or intuition can play an important role. It is impossible in principle, due to the nature of the data, to specify a criterion and procedure to obtain an ideal fuzzy model. Instead of such a non-interactive approach, our effort should be directed to develop a method which makes it possible to observe data scattered in a multi-dimensional space. The main subject of fuzzy modeling is how to analyze data in order to summarize it to a certain extent so that we can judge quality of our model by intuition. The main proposal in this paper is a clustering technique which takes into account both continuity and linearity of the data distribution. We call this technique the hyperellipsoidal clustering method, which assists modelers in finding fuzzy subsets suitable for building a fuzzy model. We will deal with other problems in fuzzy modeling as well, such as the effect of data standardization, the selection of conditional and explanatory variables, the shape of a membership function and its tuning problem, the manner of evaluating weights of rules, and the simulation technique for verifying a fuzzy model.