The pseudo-information entropy of Z-number and its applications in multi-attribute decision-making

Abstract

In order to find a reasonable and effective approach to describe the information contained in a specific Z-number, we introduce information entropy into Z-number environment in this paper, and investigate its applications in multi-attribute decision-making (MADM) issues. Moreover, aiming at the problem with the weighting indicated by Z-number values, we propose two novel weighting methodologies based on conditional entropy and sigmoid function, respectively. Firstly, on the basis of the maximum entropy principle, the optimization model to calculate the underlying probability distribution of Z-number is introduced. And then, we define Z-number pseudo-information entropy, and a novel Z-VIKOR method is proposed to solve a selecting regional circular economy development plan issue from the perspective of information entropy. Furthermore, we propose Z-number pseudo-conditional entropy, and the relationship between Z-number pseudo-information entropy and Z-number pseudo-conditional entropy is investigated. Subsequently, a weighting method based on information entropy of Z-number is proposed. In addition, we also introduce the weighting approach based on the sigmoid function decision-making method. Finally, we introduce a government new energy investment problem to verify and compare the effectiveness of the new weighting approaches. The new method gives a solution to the problem related to Z-number from the perspective of information entropy.