Article
Version 1
This version is not peer-reviewed
An Exploration on Z-Number and Its Properties
Version 1
: Received: 11 July 2024 / Approved: 11 July 2024 / Online: 11 July 2024 (09:58:12 CEST)
How to cite: Jiang, G.; Shen, X.; Liao, X.; Xuan, X.; Wu, L.; Zhang, H.; Li, Z. An Exploration on Z-Number and Its Properties. Preprints 2024, 2024070939. https://doi.org/10.20944/preprints202407.0939.v1 Jiang, G.; Shen, X.; Liao, X.; Xuan, X.; Wu, L.; Zhang, H.; Li, Z. An Exploration on Z-Number and Its Properties. Preprints 2024, 2024070939. https://doi.org/10.20944/preprints202407.0939.v1
Abstract
For better solving both fuzziness and reliability occurring in practical issues simultaneously, Z-number deserves further exploration under uncertainty environment. Based on the credibility distribution and conversion rules, we define its expected value, variance, and semi-variance, and realize the feasibility of calculation by deriving calculation formulas. Moreover, we delve into three characteristics inherent in symmetrical Z-numbers. The link that followed between the variance and the semi-variance of Z-numbers is discovered and proved. Furthermore, we apply the formulas of expected value and variance on Z-numbers to examples, whose consequences validate our proposed formulas. The findings indicate the significance of our study in applying the expected value and variance of fuzzy sets across diverse fields.
Keywords
Z-numbers; expected value; variance; semi-variance
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment
