The Operational Laws of Symmetric Triangular Z-Numbers

Autor: Hui Li, Xuefei Liao, Zhen Li, Lei Pan, Meng Yuan, Ke Qin
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: Mathematics, Vol 12, Iss 10, p 1443 (2024)
Druh dokumentu: article
ISSN: 12101443
2227-7390
DOI: 10.3390/math12101443
Popis: 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.
Databáze: Directory of Open Access Journals
Externí odkaz:
Nepřihlášeným uživatelům se plný text nezobrazuje