Uncertainty Measurement For Intuitionistic Fuzzy Ordered In- Formation Systems

Rough set theory is a mathematical tool for dealing with uncertain, imprecise and incom-plete information, which is raised by Pawlak (Polish Mathematician) in 1980s. In this theory, there are mainly two methodologies dealing with uncertainty measurement issue:pure rough set approach and information theory approach. Intuitionistic fuzzy sets which can describe the fuzzy phenomenon more objectively and exquisitely are the spread of the fuzzy sets. This article which is on the intuitionistic fuzzy ordered information systems, constructs four classes of the upper and lower approximation operators basing on the dominance intuitionistic fuzzy infor-mation systems and measures the uncertainty of the intuitionistic fuzzy ordered information systems from the algebra viewpoint and the information viewpoint. Details are as followsFrom the algebra viewpoint, this article constructs four classes of the upper and lower approximation operators by rough set theoretic methods, discusses their relationships and in-troduces corresponding accuracy measurement and the roughness measurement. It is proved that the accuracy increase according to knowledge granularity become finer, while the rough-ness opposite. As a result, all of these four classes can be used to measure the uncertainty of intuitionistic fuzzy information systems.This article, adopting the information theory and basing on the information view, con-structs four uncertainty measurements and they are knowledge information entropy, knowledge granularity measurement, knowledge elementary entropy and knowledge rough entropy. It is tested that the four classes of measurements are monotonicity with the finer of knowledge gran-ularity and they have boundedness. After all, they can be used to testify the uncertainty of intuitionistic fuzzy information systems and we can get the corresponding relationship of the four classes by analysis and comparison.