Aggregation Operators on Pythagorean Fuzzy Hypersoft Matrices With Application in the Selection of Wastewater Treatment Plants
Pythagorean fuzzy hypersoft sets (PFHSSs) are a novel model that is projected to address the limitations of Pythagorean fuzzy soft sets (PFSSs) regarding the entitlement of a multi-argument domain for the approximation of parameters under consideration. It is more flexible and reliable as it conside...
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2024-01-01
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| author | Muhammad Naveed Jafar Kainat Muniba Khan Miin-Shen Yang |
| author_facet | Muhammad Naveed Jafar Kainat Muniba Khan Miin-Shen Yang |
| author_sort | Muhammad Naveed Jafar |
| collection | DOAJ |
| description | Pythagorean fuzzy hypersoft sets (PFHSSs) are a novel model that is projected to address the limitations of Pythagorean fuzzy soft sets (PFSSs) regarding the entitlement of a multi-argument domain for the approximation of parameters under consideration. It is more flexible and reliable as it considers the further classification of parameters into their relevant parametric valued sets. This article aims to be multi-faced. Firstly, several axiomatic properties, operational results, and aggregation operations on PFHSSs will be developed. Secondly, matrices are developed for PFHSSs, called Pythagorean fuzzy hypersoft matrices (PFHSMs). The essential basic properties and aggregation operations of PFHSMs are then characterized with the support of numerical examples. Thirdly, the matrix theory of PFHSSs is implemented in real-world decision-making scenarios for Mobile selection using the proposed choice matrix theory. At the end of the article, we go on a real-life problem for wastewater treatment. Wastewater treatment is crucial for preserving the environment and public health. It comprises purifying wastewater of contaminants and pollutants so that it may be utilized for other things or discharged safely into the environment. It is essential to protect the environment and the public health by removing toxins from domestic, industrial, and commercial sewages. We finally apply our proposed algorithm in the selection of wastewater treatment plants by employing the proposed algorithm based on PFHSMs. In fact, PFHSMs are flexible enough to be used in a wide range of fields, including image processing, expert systems, pattern recognition, and medical diagnosis. The future directions are discussed with these PFHSMs to develop MCDM techniques such as TOPSIS, VIKOR, and SAW so that they can be applied in a wider range of fields. |
| format | Article |
| id | doaj-art-11423ecc02574728aa44f27b1d4877e4 |
| institution | Kabale University |
| issn | 2169-3536 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj-art-11423ecc02574728aa44f27b1d4877e42025-08-20T03:26:20ZengIEEEIEEE Access2169-35362024-01-01123187319910.1109/ACCESS.2023.334734910374085Aggregation Operators on Pythagorean Fuzzy Hypersoft Matrices With Application in the Selection of Wastewater Treatment PlantsMuhammad Naveed Jafar0https://orcid.org/0000-0002-7633-6497Kainat Muniba Khan1Miin-Shen Yang2https://orcid.org/0000-0002-4907-3548Department of Mathematics, University of Management and Technology, Lahore, PakistanDepartment of Environmental Science and Policy, Lahore School of Economics, Lahore, PakistanDepartment of Applied Mathematics, Chung Yuan Christian University, Zhongli, Taoyuan, TaiwanPythagorean fuzzy hypersoft sets (PFHSSs) are a novel model that is projected to address the limitations of Pythagorean fuzzy soft sets (PFSSs) regarding the entitlement of a multi-argument domain for the approximation of parameters under consideration. It is more flexible and reliable as it considers the further classification of parameters into their relevant parametric valued sets. This article aims to be multi-faced. Firstly, several axiomatic properties, operational results, and aggregation operations on PFHSSs will be developed. Secondly, matrices are developed for PFHSSs, called Pythagorean fuzzy hypersoft matrices (PFHSMs). The essential basic properties and aggregation operations of PFHSMs are then characterized with the support of numerical examples. Thirdly, the matrix theory of PFHSSs is implemented in real-world decision-making scenarios for Mobile selection using the proposed choice matrix theory. At the end of the article, we go on a real-life problem for wastewater treatment. Wastewater treatment is crucial for preserving the environment and public health. It comprises purifying wastewater of contaminants and pollutants so that it may be utilized for other things or discharged safely into the environment. It is essential to protect the environment and the public health by removing toxins from domestic, industrial, and commercial sewages. We finally apply our proposed algorithm in the selection of wastewater treatment plants by employing the proposed algorithm based on PFHSMs. In fact, PFHSMs are flexible enough to be used in a wide range of fields, including image processing, expert systems, pattern recognition, and medical diagnosis. The future directions are discussed with these PFHSMs to develop MCDM techniques such as TOPSIS, VIKOR, and SAW so that they can be applied in a wider range of fields.https://ieeexplore.ieee.org/document/10374085/Fuzzy setspythagorean fuzzy sets (PFSs)pythagorean fuzzy soft sets (PFSSs)pythagorean fuzzy hypersoft sets (PFHSSs)pythagorean fuzzy hypersoft matrices (PFHSMs) |
| spellingShingle | Muhammad Naveed Jafar Kainat Muniba Khan Miin-Shen Yang Aggregation Operators on Pythagorean Fuzzy Hypersoft Matrices With Application in the Selection of Wastewater Treatment Plants IEEE Access Fuzzy sets pythagorean fuzzy sets (PFSs) pythagorean fuzzy soft sets (PFSSs) pythagorean fuzzy hypersoft sets (PFHSSs) pythagorean fuzzy hypersoft matrices (PFHSMs) |
| title | Aggregation Operators on Pythagorean Fuzzy Hypersoft Matrices With Application in the Selection of Wastewater Treatment Plants |
| title_full | Aggregation Operators on Pythagorean Fuzzy Hypersoft Matrices With Application in the Selection of Wastewater Treatment Plants |
| title_fullStr | Aggregation Operators on Pythagorean Fuzzy Hypersoft Matrices With Application in the Selection of Wastewater Treatment Plants |
| title_full_unstemmed | Aggregation Operators on Pythagorean Fuzzy Hypersoft Matrices With Application in the Selection of Wastewater Treatment Plants |
| title_short | Aggregation Operators on Pythagorean Fuzzy Hypersoft Matrices With Application in the Selection of Wastewater Treatment Plants |
| title_sort | aggregation operators on pythagorean fuzzy hypersoft matrices with application in the selection of wastewater treatment plants |
| topic | Fuzzy sets pythagorean fuzzy sets (PFSs) pythagorean fuzzy soft sets (PFSSs) pythagorean fuzzy hypersoft sets (PFHSSs) pythagorean fuzzy hypersoft matrices (PFHSMs) |
| url | https://ieeexplore.ieee.org/document/10374085/ |
| work_keys_str_mv | AT muhammadnaveedjafar aggregationoperatorsonpythagoreanfuzzyhypersoftmatriceswithapplicationintheselectionofwastewatertreatmentplants AT kainatmunibakhan aggregationoperatorsonpythagoreanfuzzyhypersoftmatriceswithapplicationintheselectionofwastewatertreatmentplants AT miinshenyang aggregationoperatorsonpythagoreanfuzzyhypersoftmatriceswithapplicationintheselectionofwastewatertreatmentplants |