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Pythagorean Fuzzy Einstein Aggregation Operators with Z-Numbers: Application in Complex Decision Aid Systems

Shahzad Noor Abbasi1, Shahzaib Ashraf1,*, M. Shazib Hameed1, Sayed M. Eldin2,*

1 Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan, 64200, Pakistan
2 Center of Research, Faculty of Engineering, Future University in Egypt, New Cairo, 11835, Egypt

* Corresponding Authors: Shahzaib Ashraf. Email: email; Sayed M. Eldin. Email: email

(This article belongs to this Special Issue: Advanced Computational Models for Decision-Making of Complex Systems in Engineering)

Computer Modeling in Engineering & Sciences 2023, 137(3), 2795-2844.


The primary goal of this research is to determine the optimal agricultural field selection that would most effectively support manufacturing producers in manufacturing production while accounting for unpredictability and reliability in their decision-making. The PFS is known to address the levels of participation and non-participation. To begin, we introduce the novel concept of a PFZN, which is a hybrid structure of Pythagorean fuzzy sets and the ZN. The PFZN is graded in terms of membership and non-membership, as well as reliability, which provides a strong advice in real-world decision support concerns. The PFZN is a useful tool for dealing with uncertainty in decision-aid problems. The PFZN is a practical way for dealing with such uncertainties in decision-aid problems. The list of aggregation operators: PFZN Einstein weighted averaging and PFZN Einstein weighted geometric, is established under the novel Pythagorean fuzzy ZNs. It is a more precise mathematical instrument for dealing with precision and uncertainty. The core of this research is to develop a numerical algorithm to tackle the uncertainty in real-life problems using PFZNs. To show the applicability and effectiveness of the proposed algorithm, we illustrate the numerical case study related to determining the optimal agricultural field. The main purpose of this work is to describe the extended EDAS approach, then compare the proposed methodology with many other methodologies now in use, and then demonstrate how the suggested methodology may be applied to real-world problems. In addition, the final ranking results that were obtained by the devised techniques were more efficient and dependable in comparison to the results provided by other methods presented in the literature.


Cite This Article

Abbasi, S. N., Ashraf, S., Hameed, M. S., Eldin, S. M. (2023). Pythagorean Fuzzy Einstein Aggregation Operators with Z-Numbers: Application in Complex Decision Aid Systems. CMES-Computer Modeling in Engineering & Sciences, 137(3), 2795–2844.

cc 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.
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