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The Operational Laws of Symmetric Triangular Z-Numbers

Author

Listed:
  • Hui Li

    (School of Economics, Shanghai University, Shanghai 200444, China)

  • Xuefei Liao

    (School of Economics and Management, Zhejiang Ocean University, Zhoushan 316022, China)

  • Zhen Li

    (School of Logistics and Maritime Studies, Bahrain Polytechnic, Isa Town 33349, Bahrain)

  • Lei Pan

    (School of Management, Shanghai University, Shanghai 200444, China)

  • Meng Yuan

    (Qian Weichang College, Shanghai University, Shanghai 200444, China)

  • Ke Qin

    (School of Management, Shanghai University, Shanghai 200444, China)

Abstract

To model fuzzy numbers with the confidence degree and better account for information uncertainty, Zadeh came up with the notion of Z-numbers, which can effectively combine the objective information of things with subjective human interpretation of perceptive information, thereby improving the human comprehension of natural language. Although many numbers are in fact Z-numbers, their higher computational complexity often prevents their recognition as such. In order to reduce computational complexity, this paper reviews the development and research direction of Z-numbers and deduces the operational rules for symmetric triangular Z-numbers. We first transform them into classical fuzzy numbers. Using linear programming, the extension principle of Zadeh, the convolution formula, and fuzzy number algorithms, we determine the operational rules for the basic operations of symmetric triangular Z-numbers, which are number-multiplication, addition, subtraction, multiplication, power, and division. Our operational rules reduce the complexity of calculation, improve computational efficiency, and effectively reduce the information difference while being applicable to other complex operations. This paper innovatively combines Z-numbers with classical fuzzy numbers in Z-number operations, and as such represents a continuation and innovation of the research on the operational laws of Z-numbers.

Suggested Citation

  • Hui Li & Xuefei Liao & Zhen Li & Lei Pan & Meng Yuan & Ke Qin, 2024. "The Operational Laws of Symmetric Triangular Z-Numbers," Mathematics, MDPI, vol. 12(10), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1443-:d:1390191
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    References listed on IDEAS

    as
    1. R. A. Aliev & O. H. Huseynov & R. Serdaroglu, 2016. "Ranking of Z-Numbers and Its Application in Decision Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(06), pages 1503-1519, November.
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