New definition of the cross entropy based on the Dempster-Shafer theory and its application in a decision-making process

Cross entropy is an important index for determining the divergence between two sets or distributions. Most existing cross entropy are proposed in a fuzzy environment and undefined in some uncertain situations (e.g., Dempster-Shafer theory). This study proposes an extended cross entropy measure of belief values based on a belief degree using available evidence. Thus, a new aspect of belief functions represents in the name of a belief set. Then, a new cross entropy measure between two belief sets is defined. Furthermore, the application of the cross-entropy measure in multi-criteria decision making (MCDM) is provided with belief valued information.