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 .
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  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.
SourceAvailable from: Piotr Prokopowicz
Article: Ordered fuzzy numbers[Show abstract] [Hide abstract]
ABSTRACT: Fuzzy counterpart of real numbers is presented. Fuzzy membership functions, which satisfy conditions similar to the quasi-convexity are considered. An extra feature, called the orientation of the curve of fuzzy membership function, is introduced. It leads to a novel concept of an ordered fuzzy number, represented by the ordered pair of real continuous functions. Arithmetic operations defined on ordered fuzzy numbers enable to avoid some drawbacks of the classical approach.Bulletin of the Polish Academy of Sciences Mathematics 01/2003; 51.