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

Nik Muhammad Farhan Hakim Nik Badrul Alam, Ku Muhammad Naim Ku Khalif, Nor Izzati Jaini, Alexander Gegov

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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.

Original languageEnglish
Article number400
Number of pages24
JournalInformation (Switzerland)
Issue number7
Publication statusPublished - 13 Jul 2023


  • fuzzy decision making
  • fuzzy ranking
  • multi-criteria decision making
  • SWOT
  • Z-number

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