Research Seminar - March 17, 2000

Seminar Announcement

Abstract

The main challenge in Artificial Intelligence is to cope with problems of very high complexity. Even if an analytical model of the system in question exists, it is computationally impossibl eto use it when doing real time control or decision making.

Soft Computing, including fuzzy systems and Artificial Neural Networks offers several tools to treat such problems, a common feature is that apporoximation of the model and of the necessary transfer functions is done, usually in a very human friendly way. The mathematical roots of this kind of approximation go back to Hilbert's Conjecture about decomposition, Kolmogorov's theorem, and many results in the 1970-s and 1980-s that have been published especially in the NN context. From the early 1990-s, also fuzzy approximation theorems were established.

A rather general fram of this kind of approximation is the Tikhonov-interpolation, of which Shepard-interpolation is a very important special type. In the early 1990-s Koczy and Hirota introduced a family of fuzzy rule interpolation methods that turned out to be generalisations of the latter, and had very advantageous convergence and stability properties.

In very complex systems, interpolation and the use of sparse rule bases was not enough for an effective reduction of the complexity, so Sugeno etv al. suggested the use of a naturally constructed hierarchically structured rule base type. This worked well with the unmanned helicopter experiment.

Combination of the two reduction approaches, interpolation and hierarchy was suggested by Koczy and Hirota in 1993 and 1996. The talk will treat this combined methos in detail.

A most intriguing question is how such complex models can be automatically identified, when there is no such obvious natural structure in the problem, as in the case of the helicopter. We suggest a novel approach, where input-output data is clustered with the c-means method of Bezdek (like in the method of Sugeno and Yasukawa), but instead of only using the outputs for establishing the clusters, all projections of the data will be separately analysed. The use of projections reduces the amount of data taken into consideration in one clustering turn. It will be shown, how from these cluster projections, dense or sparse fuzzy rule bases will be built up.

Reference will be done to some potential applications.