Relative entropy of Z-numbers

Abstract Real-world information is characterized by uncertainty and partial reliability. In order to model this information, Zadeh introduced the concept of Z-numbers. It has been a challenge to construct a mathematical model to handle Z-number-based information similar to probability theory. One of the basic concepts in probability theory is relative entropy, also known as Kullback-Leibler divergence and information divergence, which is directed divergence between two probability distributions. In this work, we propose an approach for the development of the concept of relative entropy of Z-numbers. It based on the essence of Z-numbers, maximum entropy method and the relative entropy of probability distributions. Based on the proposed relative entropy, we construct a novel Technique for Order of Preference by Similarity to Ideal Solution based on the Z-numbers (Z-TOPSIS) method, which directly calculates Z-numbers instead of converting them to fuzzy numbers. A case study of supplier selection is then used to illustrate the effectiveness of our proposed Z-TOPSIS method.