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 is 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.

现实世界的信息具有不确定性和部分可靠性的特点。为了对这些信息建模，Zadeh 引入了 Z 数的概念。构建一个数学模型来处理类似于概率论的基于 Z 数的信息一直是一个挑战。概率论中的基本概念之一是相对熵，也称为 Kullback-Leibler 散度和信息散度，即两个概率分布之间的有向散度。在这项工作中，我们提出了一种发展 Z 数相对熵概念的方法。它基于Z数的本质，最大熵方法和概率分布的相对熵。基于所提出的相对熵，我们基于 Z 数 (Z-TOPSIS) 方法构建了一种新的通过与理想解相似的偏好顺序技术，该技术直接计算 Z 数而不是将它们转换为模糊数。然后使用供应商选择的案例研究来说明我们提出的 Z-TOPSIS 方法的有效性。