A new interval-valued knowledge measure for interval-valued intuitionistic fuzzy sets and application in decision making

• A new knowledge measure for interval-valued intuitionistic fuzzy sets.
• A generalization of the knowledge measure for intuitionistic fuzzy sets.
• Unlike to other measures, it is defined as an interval knowledge measure.
• Reliable measure for uncertain fuzzy information in multi-attribute group decision making.

In this paper, firstly we discuss some entropy measures for the interval-valued intuitionistic fuzzy sets (IvIFSs). Then we extend the knowledge measure for the intuitionistic fuzzy sets (IFSs) to propose a new interval-valued knowledge measure for the IvIFSs. Based on the proposed knowledge measure we construct a new interval-valued information entropy measure for IvIFSs, which is an extended notion of the entropy measures for IFSs. The proposed knowledge measure is defined as an interval of amounts of knowledge measured on an IvIFS, related to the uncertain information in terms of interval membership degree and interval non-membership degree. In comparison with other existing measures, it seems to be simpler and more intuitively appealing. Several illustrative examples are performed to demonstrate the effectiveness and practicality of the proposed method in handling with the increasing complexity of the decision making problems.