Preference and attitude in parameterized knowledge measure for decision making under uncertainty

We develop in this paper a novel entropy-independent knowledge measure (KM), with which to reveal some significant aspects of psychological cognition hidden in the handling of intuitionistic fuzzy sets (IFSs). We briefly discuss the two facets of knowledge associated with an IFS, i.e., the information content and the information clarity. We then establish, based on the latest axiomatic definition of KM in the context of IFSs, a novel parameterized KM in which two significant aspects of psychological cognition are considered, personal attitude and preference to be exact. We believe that the KM provided in this manner could truly capture the unique features of an IFS, including the potential knowledge related to the specificity and non-specificity of an IFS, the amount of which depends actually on users’ character traits. The developed KM is equipped with two parameters, one of which expresses the type of attitude towards the non-specificity of an IFS while the other indicates the degree of personal preference between those two facets of knowledge. We also show that some existing measures can be obtained as particular cases of this general model. Finally, we illustrate the application of this measure in decision making under uncertainty.