The Operational Laws of Symmetric Triangular Z-Numbers

Hui Li, Xuefei Liao (), Zhen Li, Lei Pan, Meng Yuan and Ke Qin
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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

Mathematics, 2024, vol. 12, issue 10, 1-18

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.

Keywords: Z-numbers; symmetric triangular fuzzy numbers; operational laws (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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