A new method to measure the knowledge amount of Atanassov’s intuitionistic fuzzy sets

It is of great significance to measure the knowledge amount conveyed by Atanassov’s intuitionistic fuzzy sets (AIFSs). Many efforts have been done to define a suitable knowledge measure for AIFSs, or uncertainty measure, named as a dual measure of knowledge measure. However, many of these measures are developed from the view of point of intuitionistic fuzzy entropy, which cannot well reflect the knowledge amount associated with an AIFS. Other knowledge measures developed based on the difference between an AIFS and its complement may lead to information loss in the scenario of decision making. This paper proposed a new knowledge measure for AIFSs. The axiomatic definition of knowledge measure is extended to a more general level. The properties of the new developed knowledge measure are investigated through mathematical analysis and numerical examples. Further discussion on the relation between knowledge measure and entropy measure is proposed to clear up the relation and distinction between them.