Cross-Entropy of Dual Hesitant Fuzzy Sets for Multiple Attribute Decision-Making

This paper proposes a cross-entropy measure between dual hesitant fuzzy sets (DHFSs) as an extension of the cross-entropy measures of intuitionistic fuzzy sets. Then the cross-entropy measure between DHFSs is applied to multiple attribute decision making under dual hesitant fuzzy environments. Through the weighted cross-entropy measure between each alternative and the ideal alternative, we can obtain the ranking order of all alternatives and the best one. The decision-making method based on the cross-entropy measure of DHFSs can deal with dual hesitant fuzzy multiple attribute decision making problems and can automatically take into account much more information than existing hesitant (or intuitionistic) fuzzy decision-making methods and the differences of the evaluation data given by different experts or decision makers. Finally, a practical example about investment alternatives is given to demonstrate the application and effectiveness of the developed approach.