Reference set design for relational modeling of fuzzy systems

Tibor Lapohos; Ralph O. Buchal

doi:10.1117/12.188912

10 October 1994 Reference set design for relational modeling of fuzzy systems

Tibor Lapohos, Ralph O. Buchal

Proceedings Volume 2353, Intelligent Robots and Computer Vision XIII: Algorithms and Computer Vision; (1994) https://doi.org/10.1117/12.188912
Event: Photonics for Industrial Applications, 1994, Boston, MA, United States

Abstract

One of the keys to the successful relational modeling of fuzzy systems is the proper design of fuzzy reference sets. This has been discussed throughout the literature. In the frame of modeling a stochastic system, we analyze the problem numerically. First, we briefly describe the relational model and present the performance of the modeling in the most trivial case: the reference sets are triangle shaped. Next, we present a known fuzzy reference set generator algorithm (FRSGA) which is based on the fuzzy c-means (Fc-M) clustering algorithm. In the second section of this chapter we improve the previous FRSGA by adding a constraint to the Fc-M algorithm (modified Fc-M or MFc-M): two cluster centers are forced to coincide with the domain limits. This is needed to obtain properly shaped extreme linguistic reference values. We apply this algorithm to uniformly discretized domains of the variables involved. The fuzziness of the reference sets produced by both Fc-M and MFc-M is determined by a parameter, which in our experiments is modified iteratively. Each time, a new model is created and its performance analyzed. For certain algorithm parameter values both of these two algorithms have shortcomings. To eliminate the drawbacks of these two approaches, we develop a completely new generator algorithm for reference sets which we call Polyline. This algorithm and its performance are described in the last section. In all three cases, the modeling is performed for a variety of operators used in the inference engine and two defuzzification methods. Therefore our results depend neither on the system model order nor the experimental setup.

Citation Download Citation

Tibor Lapohos and Ralph O. Buchal "Reference set design for relational modeling of fuzzy systems", Proc. SPIE 2353, Intelligent Robots and Computer Vision XIII: Algorithms and Computer Vision, (10 October 1994); https://doi.org/10.1117/12.188912

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