Uncertainty measure of Atanassov's intuitionistic fuzzy 𝒯 equivalence information systems

Abstract

Atanassov's intuitionistic fuzzy 𝒯 equivalence information systems are natural extensions of fuzzy 𝒯 equivalence information systems. The aim of this paper is to investigate the uncertainty measures of knowledge in Atanassov's intuitionistic fuzzy 𝒯 equivalence information systems. At the first, we introduce the concepts of knowledge granulation, knowledge entropy and knowledge uncertainty measure in Atanassov's intuitionistic fuzzy 𝒯 equivalence information systems, and some important properties of them are studied. From these properties, it can be shown that these measures provide important approaches to measuring the discernibility ability of different knowledge in Atanassov's intuitionistic fuzzy 𝒯 equivalence information systems. And relationships among knowledge granulation, knowledge entropy and knowledge uncertainty measure are considered. Furthermore, we introduce the definition of rough entropy of rough sets in Atanassov's intuitionistic fuzzy 𝒯 equivalence information systems. By an example, it is shown that the rough entropy of rough set is more accurate than natural extension of classical rough degree to measure the roughness of rough set in Atanassov's intuitionistic fuzzy 𝒯 equivalence information systems.