Hybrid weighted arithmetic and geometric averaging operator of cubic Z-numbers and its decision-making method

Abstract

A Z-number (ZN) presented by Zadeh is a new framework of fuzzy sets that combines a restriction value with a reliability measure. Based on this motivation of the concept of ZN, this study first proposes a cubic Z-number (CZN) set and operational relations of CZNs, and then defines two expected functions of CZNs to rank CZNs. Next, we present a CZN hybrid weighted arithmetic and geometric averaging (CZNHWAGA) operator and its properties. Then, a multicriteria DM model with unknown criterion weights is established based on the proposed CZNHWAGA operator, the expected functions, and the standard deviation of the expected values in the setting of CZNs. Lastly, the established DM model is applied to the selection of solar cells to illustrate its practicability and effectiveness in the setting of CZNs. However, the established DM model can solve the problem of unknown criterion weights and strengthen the DM reliability and flexibility.

KEYWORDS:

• Cubic Z-number
• expected function
• cubic Z-number hybrid weighted arithmetic and geometric averaging operator
• decision making
• solar cell

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Jun Ye

Jun Ye received his M.S. degree in Automation and Robotics from the Technical University of Koszalin, Poland in 1997. In 2012, he was a visiting scholar in the School of Engineering of Southern Polytechnic State University in USA. Now, he is a professor in Ningbo University, China. He has more than 30 years of experience in teaching and research. His research interests include neutrosophic theory and applications, soft computing, decision making theory and method, intelligent control, robotics, pattern recognitions, rock mechanics, and fault diagnosis. He has published more than 290 papers in journals. He was selected as ‘Elsevier Chinese Most Cited Researchers’ in 2019, 2020, 2021.

Shigui Du

Shi-Gui Du got his Ph.D. from Zhejiang University, China in 1999, and received his B.S. degree from China University of Geosciences, China in 1984. He is presently a professor at Ningbo University. His research interests include geotechnical engineering, rock mechanics, mining sciences, fuzzy theory, and engineering management. He has published more than 200 papers in journals.

Rui Yong

Rui Yong got his Ph.D. from China University of Geosciences, China in 2014, and received his B.S. degree from China University of Geosciences, China in 2009. He is presently a professor at Ningbo University. His research interests include geotechnical engineering, fuzzy theory, decision making, and engineering management. He has published more than 60 papers in journals.