The directed compatibility between ordered fuzzy numbers-A base tool for a direction sensitive fuzzy information processing

Abstract

The Ordered Fuzzy Numbers (OFN) were defined over 10 years ago as a tool for processing fuzzy numbers. This model has an additional feature used in processing, namely direction. It allows to define arithmetical operations in a new way. Proposed methods retain the basic computational properties of the operations known for the real numbers. Apart from a good calculations, OFNs also offer new possibilities for processing imprecise information. The new property- A direction-has a major impact on the calculations, but gives also a new potential for processing data in the fuzzy systems. We can include to the fuzzy value some more interpretation than membership value. If we want take into account this additional information in the processing of fuzzy system, we need the methods which are sensitive for the direction. This publication presents the basic tool for processing a fuzzy statement 'A is B' where A and B are OFNs. It can be called a compatibility of A with B. New proposition is sensitive for the direction and bases on the conception of the Direction Determinant proposed in previous studies on the topic.