Open Access


Aggregation Operators for Interval-Valued Pythagorean Fuzzy Hypersoft Set with Their Application to Solve MCDM Problem

Rana Muhammad Zulqarnain1, Imran Siddique2, Rifaqat Ali3, Fahd Jarad4,5,6,*, Aiyared Iampan7
1 Department of Mathematics, University of Management and Technology, Sialkot Campus, Lahore, 51310, Pakistan
2 Department of Mathematics, University of Management and Technology, Lahore, 54000, Pakistan
3 Department of Mathematics, College of Science and Arts, King Khalid University, Abha, 61413, Saudi Arabia
4 Department of Mathematics, Cankaya University, Ankara, 06790, Turkey
5 Department of Mathematics, King Abdulaziz University, Jeddah, 22254, Saudi Arabia
6 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 404332, Taiwan
7 Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao, 56000, Thailand
* Corresponding Author: Fahd Jarad. Email:
(This article belongs to this Special Issue: Decision making Modeling, Methods and Applications of Advanced Fuzzy Theory in Engineering and Science)

Computer Modeling in Engineering & Sciences 2023, 135(1), 619-651.

Received 24 March 2022; Accepted 18 May 2022; Issue published 29 September 2022


Experts use Pythagorean fuzzy hypersoft sets (PFHSS) in their investigations to resolve the indeterminate and imprecise information in the decision-making process. Aggregation operators (AOs) perform a leading role in perceptivity among two circulations of prospect and pull out concerns from that perception. In this paper, we extend the concept of PFHSS to interval-valued PFHSS (IVPFHSS), which is the generalized form of interval-valued intuitionistic fuzzy soft set. The IVPFHSS competently deals with uncertain and ambagious information compared to the existing interval-valued Pythagorean fuzzy soft set. It is the most potent method for amplifying fuzzy data in the decision-making (DM) practice. Some operational laws for IVPFHSS have been proposed. Based on offered operational laws, two inventive AOs have been established: interval-valued Pythagorean fuzzy hypersoft weighted average (IVPFHSWA) and interval-valued Pythagorean fuzzy hypersoft weighted geometric (IVPFHSWG) operators with their essential properties. Multi-criteria group decision-making (MCGDM) shows an active part in contracts with the difficulties in industrial enterprise for material selection. But, the prevalent MCGDM approaches consistently carry irreconcilable consequences. Based on the anticipated AOs, a robust MCGDM technique is deliberate for material selection in industrial enterprises to accommodate this shortcoming. A real-world application of the projected MCGDM method for material selection (MS) of cryogenic storing vessels is presented. The impacts show that the intended model is more effective and reliable in handling imprecise data based on IVPFHSS.


Interval-valued pythagorean fuzzy hypersoft set; IVPFHSWA operator; IVPFHSWG operator; MCGDM

Cite This Article

Zulqarnain, R. M., Siddique, I., Ali, R., Jarad, F., Iampan, A. (2023). Aggregation Operators for Interval-Valued Pythagorean Fuzzy Hypersoft Set with Their Application to Solve MCDM Problem. CMES-Computer Modeling in Engineering & Sciences, 135(1), 619–651.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
  • 160


  • 149


  • 0


Share Link

WeChat scan