The Application of Z-Numbers in Fuzzy Decision Making: The State of the Art

Abstract

A Z-number is very powerful in describing imperfect information, in which fuzzy numbers are paired such that the partially reliable information is properly processed. During a decision-making process, human beings always use natural language to describe their preferences, and the decision information is usually imprecise and partially reliable. The nature of the Z-number, which is composed of the restriction and reliability components, has made it a powerful tool for depicting certain decision information. Its strengths and advantages have attracted many researchers worldwide to further study and extend its theory and applications. The current research trend on Z-numbers has shown an increasing interest among researchers in the fuzzy set theory, especially its application to decision making. This paper reviews the application of Z-numbers in decision making, in which previous decision-making models based on Z-numbers are analyzed to identify their strengths and contributions. The decision making based on Z-numbers improves the reliability of the decision information and makes it more meaningful. Another scope that is closely related to decision making, namely, the ranking of Z-numbers, is also reviewed. Then, the evaluative analysis of the Z-numbers is conducted to evaluate the performance of Z-numbers in decision making. Future directions and recommendations on the applications of Z-numbers in decision making are provided at the end of this review.

Development of the method of general interpolation for Z-number-valued if-then rules

“…However, future research on Z-numbers may include extensions of MCDM (multi-criteria decision-making) models based on these generalized Z-numbers: intuitionistic Z-numbers, neutrosophic Z-numbers, Pythagorean Z-numbers, and Fermatean Z-numbers. These generalized Z-numbers are considered the best representation of Z-numbers and have advantages that deserve further study [18]. This will effectively identify the strengths of these generalized Z-numbers and their application in various decision-making contexts.…”

Prioritization of control measures in leakage scenario using Hendershot theory and FBWM-TOPSIS

“…The level of confidence varies according to different experts, and the uncertainty and difference in the validity of their opinions cannot be ignored [61]. The advantage of Z-Numbers compared to conventional fuzzy methods is to consider uncertainty in the opinion of experts and assign credit to their opinion for estimating fuzzy parameters [62,63]. This issue was one of the limitations of the present study, which is recommended to be considered in future studies.…”

An integrated Z-number and intuitionistic fuzzy sets for considering uncertainty in the risk assessment using the SHIPP methodology

“…Experts frequently use natural language to express their opinions on the probability of essential events in risk assessment. Still, the information used to make such decisions can often be ambiguous and only slightly reliable 17 . Zadeh introduced the notion of a fuzzy set (FS) to illustrate the ambiguity of information 18 .…”