Knowledge measure for interval-valued intuitionistic fuzzy sets and its application to decision making under uncertainty

A measure of knowledge should not be viewed simply as a dual measure of entropy in the context of intuitionistic fuzzy sets as there is no natural logic between these two kinds of measures with the introduction of hesitancy, nor in the context of interval-valued intuitionistic fuzzy sets (IVIFSs), for that matter. This work is devoted to the introduction of an axiomatic definition of knowledge measure for IVIFSs. In order to do that, a set of new axioms is presented with which knowledge measure should comply in the context of IVIFSs. A concrete model following these axioms is then developed to measure the amount of knowledge associated with an IVIFS. Two facets of knowledge associated with an IVIFS, i.e., the information content and the information clarity, are simultaneously taken into account in the construction of the model to truly reflect the nature of an IVIFS. In particular, the connection between knowledge measure and fuzzy entropy is investigated under this axiomatic framework. A series of tests is also provided to examine the performance of the developed measure. Finally, a concept of knowledge weight on attribute in multi-attribute decision making is presented and an illustrative example is used as a demonstration of the application of the developed technique to decision making under uncertainty.