The application of z-numbers in fuzzy decision making: The state of the art

• Main Authors: Nik Muhammad Farhan Hakim, Nik Badrul Alam, Ku Muhammad Naim, Ku Khalif, Nor Izzati, Jaini, Gegov, Alexander
• Format: Article
• Language: English
• Published: MDPI AG 2023
• Subjects: Q Science (General); QA Mathematics
• Online Access: http://umpir.ump.edu.my/id/eprint/38386/1/The%20application%20of%20z-numbers%20in%20fuzzy%20decision%20making_The%20state%20of%20the%20art.pdf; http://umpir.ump.edu.my/id/eprint/38386/; https://doi.org/10.3390/info14070400; https://doi.org/10.3390/info14070400
• Institution: Universiti Malaysia Pahang

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.