The directed inference for the Kosinski’s Fuzzy Number model

Abstract

The Kosinski’s Fuzzy Number (KFN) model (former name the Ordered Fuzzy Number) is a tool for processing an imprecise information interpreted in a similar way as the classical convex fuzzy numbers. The specificity of KFNs is an additional property for the fuzzy number—the direction. Thanks to that, the calculations can be done as flexibly as with real numbers. Especially, we are not doomed to get the more fuzzy results after many arithmetical operations. Apart good calculations, the direction also has additional potential in the interpretation of fuzzy data. It can be treated as a direction of process, not only the value. For example “an income is high and process is growing” is a different situation than “an income is high, but process is lowering”. The direction of KFN can be used to represent difference between these sentences. Since we deal with an additional information, there is need for the new methods which let benefit a full potential of KFNs in the modeling of linguistic data. This paper introduces algorithm of the inference operation for fuzzy rule constructed with the KFNs. Presented proposal consider the direction of values in processing. It bases on the ideas presented in previous studies on this subject—the Direction Determinant. It was proposed as the general basic tool for defining methods, where we need sensitivity for the direction.