Adaptation of rules in the fuzzy control system using the arithmetic of ordered fuzzy numbers

Abstract

This paper describes a new look on adaptation of fuzzy rules in fuzzy control process. New idea is based on properties of the Ordered Fuzzy Numbers. The Ordered fuzzy nunbers (OFN) are a new model of fuzzy numbers, presented a few years ago [15]. Important property and advantage of the new model of fuzzy numbers is simple realization of arithmetical operations. Thanks to that we can get neutral element of adding and multiplication in the same way like in real numbers. Easy way of calculating on the Ordered Fuzzy Numbers makes possible to use them in a fuzzy control process. In the [21] new methods of processing information for a fuzzy control system were presented. These methods basing on arithmetic of the Ordered Fuzzy Numbers. The goal of that paper is to present a way to use a good arithmetical properties of Ordered Fuzzy Numbers in the process of rules adaptation for the fuzzy control system. © 2008 Springer-Verlag Berlin Heidelberg.