Knowledge Measure for Atanassov's Intuitionistic Fuzzy Sets

A measure of knowledge is often viewed as a dual measure of entropy in a fuzzy system; thus, it appears that the less entropy may always accompany the greater amount of knowledge. Actually, this does not reflect the reality in the context of Atanassov's intuitionistic fuzzy sets (A-IFSs). In this paper, we introduce a novel axiomatic framework for measuring the amount of knowledge associated with A-IFSs, as opposed to a measure of fuzzy entropy. We present an axiomatic definition of knowledge measure for A-IFSs first and then develop a new robust model that strictly complies with these axioms. More efforts are made to form the main properties of two types of axioms (respectively, for fuzzy entropy and knowledge measure) into a unified framework, under which the numerical relationship between these two kinds of measures is discussed in considerable detail. This helps to clear up a fundamental misunderstanding aforementioned and ultimately to draw a firm conclusion on this topic. In particular, the developed model, for its excellent performance in experiments as well as ability to capture the unique features of A-IFSs, can be used to tackle some special problems that are difficult to handle by using fuzzy entropy alone, such as making a difference between such special cases in which there are a large number of arguments in favor but an equally large number of arguments in disapproval at the same time.