A new knowledge-based measure for intuitionistic fuzzy sets and its application in multiple attribute group decision making

Since introduced by K. Atanassov as a generalization of fuzzy sets, intuitionistic fuzzy sets (IFSs) have been investigated by many researchers and applied in many different areas, e.g. for solving multi-attribute group decision-making. It is important to find an appropriately reliable measure in order to differentiate IFSs in comparison or ranking order. Although there exist several measures, many unreasonable cases can be made by such measures. This paper introduces a new measure of amount of knowledge related to information provided in terms of IFSs. The new measure takes into account relationship between membership and non-membership degrees and hesitancy for a lack of information, making it capable to measure both degree of fuzziness and intuitionism of IFSs simultaneously. First we present a new knowledge measure for IFSs and prove some properties of the proposed measure. Based on the proposed knowledge measure we construct a new entropy measure for IFSs, a new similarity measure between IFSs and prove some properties of them. Then we use some examples to illustrate that the proposed measures, though simple in concept and calculus, can overcome the drawbacks of the existing measures. Finally, we apply the proposed knowledge measure for IFSs to deal with the multiple attribute group decision making problem.