Aggregation Operators on Pythagorean Fuzzy Hypersoft Matrices With Application in the Selection of Wastewater Treatment Plants

• Published in: IEEE access 2024, Vol.12, p.3187-3199
• Main Authors: Jafar, Muhammad Naveed, Khan, Kainat Muniba, Yang, Miin-Shen
• Format: Article
• Language: English
• Subjects: Algorithms; Contaminants; Decision making; Decision theory; Environmental protection; Expert systems; Fuzzy sets; Image processing; Matrix theory; Medical diagnosis; Operators (mathematics); Parameters; Pattern recognition; Public health; Public healthcare; pythagorean fuzzy hypersoft matrices (PFHSMs); pythagorean fuzzy hypersoft sets (PFHSSs); pythagorean fuzzy sets (PFSs); pythagorean fuzzy soft sets (PFSSs); Uncertainty; Wastewater; Wastewater treatment; Water treatment
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2023.3347349

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.