Divergence-based cross entropy and uncertainty measures of Atanassov's intuitionistic fuzzy sets with their application in decision making.

The uncertainty measure of Atanassov’s intuitionistic fuzzy sets (AIFSs) is important for information discrimination under intuitionistic fuzzy environment. Although many entropy measures and knowledge measures haven been proposed to depict uncertainty of AIFSs, how to measure the uncertainty of AIFSs is still an open topic. The relation between uncertainty and other measures like entropy measures, fuzziness and intuitionism is not clear. This paper introduces uncertainty measures by using new defined divergence-based cross entropy measure of AIFSs. Axiomatic properties of the developed uncertainty measure are analysis, together with the monotony property of uncertainty degree with respect to fuzziness and intuitionism. To adjust the contribution of fuzzy entropy and intuitionistic entropy on the total uncertainty, the proposed cross entropy and uncertainty measures are parameterized. Numerical examples indicate the effectiveness and agility of the biparametric uncertainty measure in quantifying uncertainty degree. Then we apply the cross entropy and uncertainty measures into an optimal model to determine attribute weights in multi-attribute group decision making (MAGDM) problems. A new method for intuitionistic fuzzy MAGDM problems is proposed to show the efficiency of proposed measures in applications. It is demonstrated by application examples that the proposed measures can get reasonable results coinciding with other existing methods.