Z-ACM: An approximate calculation method of Z-numbers for large data sets based on kernel density estimation and its application in decision-making

Abstract

The concept of a Z-number has obtained plenty of interest for its ability to represent uncertain and partially reliable information. Z-numbers are also widely used in decision-making for the reason that they can describe real-world information and human cognition more flexibly. However, the classical arithmetic complexity of Z-numbers is a burden in real applications, especially under large data sets. How to both retain the inherent meaning of Z-numbers and reduce the calculation complexity is a critical issue in the real Z-number-based applications. Limited theoretical progress has so far been discussed. To balance the gap between the arithmetic complexity and the inherent meaning of Z-numbers, we propose an approximate calculation method of Z-numbers (Z-ACM) based on kernel density estimation. The main ideas are as follows: first, kernel density estimation is used to partition/group Z-numbers with the total utility of Z-numbers; second, aggregate the representative Z-number in each partitioned interval using the classical arithmetic framework of Z-numbers. Based on the proposed Z-ACM, a fast decision model (FDM) is designed to deal with the issue of multi-criteria decision-making. Some examples with comparative analysis and rationality analysis are conducted to illustrate the effectiveness of the proposed methodology.