Some Generalized Aggregation Operators with Probabilistic Spherical Hesitant Fuzzy Information and Applications to Green Enterprise Credit Selection
Pub. online: 26 March 2026
Type: Research Article
Open Access
Open Access
Received
1 October 2023
1 October 2023
Accepted
1 March 2026
1 March 2026
Published
26 March 2026
26 March 2026
Abstract
In order to better solve the multi-attribute decision-making (MADM) issues in real life, this paper proposes the probabilistic spherical hesitant fuzzy set (PSHFS) theory based on spherical HFS (SHFS) and probabilistic HFS (PHFS). Firstly, PSHFS is developed, and its basic operations of PHSF element (PSHFE) are proposed. Secondly, generalized PSHF weighted averaging (GPSHFWA) and generalized PSHF weighted geometric (GPSHFWG) operators are constructed, and their excellent properties and some special forms are investigated. Thirdly, for MADM problems with different priorities of related evaluation criteria, we propose generalized PSHF prioritized weighted averaging (GPSHFPWA) and geometric (GPSHFPWG) operators, and investigate their excellent properties and some special operators. Fourthly, two new MADM techniques are constructed dependent on the proposed two types of operators in practical MADM problems. Finally, the effectiveness of the two MADM techniques constructed is tested through an application example of the green enterprise credit selection (GECS). The sensitivity analysis of parameter shows the influence on different values of parameter on the optimal alternatives by setting different parameter values, and shows the flexibility of the proposed MADM techniques. Meanwhile, the two MADM techniques are compared with several existing MADM techniques to prove the advantages of the two MADM techniques.
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Biographies
Ning Baoquan
B. Ning is a current PhD student with School of Mathematical Science, Sichuan Normal University, Chengdu, 610066, PR China. He has an MSc degree in applied mathematics from Kunming University of Science and Technology. He has published more than 30 papers in journals, such as Expert Systems with Applications, Journal of Mathematics in Practice and Theory, Fuzzy Systems and Mathematics, Logistics Technology, Science Technology and Engineering. He is currently interested in aggregation operators, decision making and computing with words.
Zhang Yalan
Y. Zhang holds an MPAcc degree in accounting from the Business School at Sichuan Normal University, China. She is an assistant researcher at West China Second University Hospital at Sichuan University.
Wei Cun
C. Wei has an MSc in applied mathematics from Southwest Petroleum University, and a PhD degree in management science and engineering from school of Management Science and Engineering at Southwestern University of Finance and Economics, China, respectively. He is a lecturer in the School of Management at Xihua University. He has published more than 30 papers in journals, such as International Journal of Intelligent Systems, Journal of Intelligent and Fuzzy Systems, IEEE Access, Mathematics, Information. He is currently interested in aggregation operators, decision making and computing with words.
Wei Guiwu
G. Wei has an MSc degree in applied mathematics from SouthWest Petroleum University, and a PhD degree in business administration from School of Economics and Management at SouthWest Jiaotong University, China, respectively. From May 2010 to April 2012, he was a postdoctoral researcher with the School of Economics and Management, Tsinghua University, Beijing, China. He is a professor in the School of Business at Sichuan Normal University. He has published more than 100 papers in journals, books and conference proceedings including journals such as Omega, Decision Support Systems, Expert Systems with Applications, Applied Soft Computing, Knowledge and Information Systems, Computers & Industrial Engineering, Knowledge-Based Systems, International Journal of Intelligent Systems, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, International Journal of Computational Intelligence Systems, International Journal of Machine Learning and Cybernetics, Fundamenta Informaticae, Informatica, Kybernetes, International Journal of Knowledge-based and Intelligent Engineering Systems and Information: An International Interdisciplinary Journal. He has published 1 book. He has participated in several scientific committees and serves as a reviewer in a wide range of journals including Computers & Industrial Engineering, International Journal of Information Technology and Decision Making, Knowledge-Based Systems, Information Sciences, International Journal of Computational Intelligence Systems and European Journal of Operational Research. He is currently interested in aggregation operators, decision making and computing with words.
