Conference Paper

Adaptation of Rules in the Fuzzy Control System Using the Arithmetic of Ordered Fuzzy Numbers

DOI: 10.1007/978-3-540-69731-2_30 Conference: Artificial Intelligence and Soft Computing - ICAISC 2008, 9th International Conference, Zakopane, Poland, June 22-26, 2008, Proceedings
Source: DBLP


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.

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    ABSTRACT: The publication shows the way of implementing arithmetic operations on fuzzy numbers based on Ordered Fuzzy Numbers calculation model \cite{Kos1}, \cite{Kos_2003}, \cite{Kos_2005}. This model allows to perform calculations on fuzzy numbers in a way that the outcomes meet the same criteria as the outcomes of calculations on real numbers. In this text, to the four basic operations with Ordered Fuzzy Numbers, a logarithm and exponentiation was added. Several examples of the calculations are included, the results of which are obvious and typical of real numbers but not achievable with the use of conventional computational methods for fuzzy numbers. From these examples one can see that the use of Ordered Fuzzy Numbers allows to obtain outcomes for real numbers in spite of using the fuzzy values.
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