Spherical fuzzy cross entropy for multiple attribute decision making problems

In this paper, we investigate the multiple attribute decision making problems with spherical fuzzy information. The advantage of spherical fuzzy set is easily reflecting the ambiguous nature of subjective judgments because the spherical fuzzy sets are suitable for capturing imprecise, uncertain and inconsistent information in the multiple attribute decision making analysis. Thus, the cross- entropy of spherical fuzzy sets called, spherical fuzzy cross-entropy, is proposed as an extension of the cross-entropy of fuzzy sets. Then, a multiple attribute decision making method based on the proposed spherical fuzzy cross entropy is established in which attribute values for alternatives are spherical fuzzy numbers. In decision making process, we utilize the spherical fuzzy weighted cross entropy between the ideal alternative and an alternative to rank the alternatives corresponding to the cross entropy values and to select the most desirable one(s). Finally, a practical example for enterprise resource planning system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.