Complex Diophantine interval-valued Pythagorean normal set for decision-making processes
Abstract A novel method for solving the multiple-attribute decision-making problem is proposed using the complex Diophantine interval-valued Pythagorean normal set (CDIVPNS). This study aims to discuss aggregating operations and how they are interpreted. We discuss the concept of CDIVPN weighted ave...
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Nature Portfolio
2025-01-01
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| Online Access: | https://doi.org/10.1038/s41598-024-82532-2 |
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| author | Murugan Palanikumar Nasreen Kausar Ponnaiah Tharaniya Željko Stević Fikadu Tesgera Tolasa |
| author_facet | Murugan Palanikumar Nasreen Kausar Ponnaiah Tharaniya Željko Stević Fikadu Tesgera Tolasa |
| author_sort | Murugan Palanikumar |
| collection | DOAJ |
| description | Abstract A novel method for solving the multiple-attribute decision-making problem is proposed using the complex Diophantine interval-valued Pythagorean normal set (CDIVPNS). This study aims to discuss aggregating operations and how they are interpreted. We discuss the concept of CDIVPN weighted averaging (CDIVPNWA), CDIVPN weighted geometric (CDIVPNWG), generalized CDIVPN weighted averaging (CGDIVPNWA) and generalized CGDIVPN weighted geometric (CGDIVPNWG). This study aimed to examine several aggregation operators using complex Diophantine interval-valued Pythagorean normal sets. We calculated the weighted average and geometric distance based on an aggregating model. We demonstrate that complex Diophantine interval-valued Pythagorean normal sets satisfy algebraic structures such as associative, distributive, idempotent, bounded, commutative and monotonic properties. In this study, we discuss the mathematical properties of the score and accuracy values. We provide an example of how enhanced score and accuracy values are used in the real world. Machine tool technology and computer science play essential roles in robots. To evaluate robotic systems, four factors must be considered such as tasks, precision, speed and completion of the work. Consequently, it is evident that the models are significantly influenced by the natural number $$\nabla$$ . To further demonstrate the effectiveness of the suggested approach, flowchart based multi-criteria decision-making is provided and applied to a numerical example. Additionally, a comparative study has been carried out to demonstrate the better results that the proposed approach provides when compared to current approaches. |
| format | Article |
| id | doaj-art-c8839320627f4404a931f06220e39d40 |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-01-01 |
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| spelling | doaj-art-c8839320627f4404a931f06220e39d402025-01-05T12:13:35ZengNature PortfolioScientific Reports2045-23222025-01-0115111910.1038/s41598-024-82532-2Complex Diophantine interval-valued Pythagorean normal set for decision-making processesMurugan Palanikumar0Nasreen Kausar1Ponnaiah Tharaniya2Željko Stević3Fikadu Tesgera Tolasa4Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha UniversityDepartment of Mathematics, Faculty of Arts and Science, Yildiz Technical UniversityDepartment of Mathematics, Rajalakshmi Institute of TechnologySchool of Industrial Management Engineering, Korea UniversityDepartment of Mathematics, Dambi Dollo UniversityAbstract A novel method for solving the multiple-attribute decision-making problem is proposed using the complex Diophantine interval-valued Pythagorean normal set (CDIVPNS). This study aims to discuss aggregating operations and how they are interpreted. We discuss the concept of CDIVPN weighted averaging (CDIVPNWA), CDIVPN weighted geometric (CDIVPNWG), generalized CDIVPN weighted averaging (CGDIVPNWA) and generalized CGDIVPN weighted geometric (CGDIVPNWG). This study aimed to examine several aggregation operators using complex Diophantine interval-valued Pythagorean normal sets. We calculated the weighted average and geometric distance based on an aggregating model. We demonstrate that complex Diophantine interval-valued Pythagorean normal sets satisfy algebraic structures such as associative, distributive, idempotent, bounded, commutative and monotonic properties. In this study, we discuss the mathematical properties of the score and accuracy values. We provide an example of how enhanced score and accuracy values are used in the real world. Machine tool technology and computer science play essential roles in robots. To evaluate robotic systems, four factors must be considered such as tasks, precision, speed and completion of the work. Consequently, it is evident that the models are significantly influenced by the natural number $$\nabla$$ . To further demonstrate the effectiveness of the suggested approach, flowchart based multi-criteria decision-making is provided and applied to a numerical example. Additionally, a comparative study has been carried out to demonstrate the better results that the proposed approach provides when compared to current approaches.https://doi.org/10.1038/s41598-024-82532-2Aggregating operatorPythagorean normal setComplex Diophantine setMultiple-attribute decision-making |
| spellingShingle | Murugan Palanikumar Nasreen Kausar Ponnaiah Tharaniya Željko Stević Fikadu Tesgera Tolasa Complex Diophantine interval-valued Pythagorean normal set for decision-making processes Scientific Reports Aggregating operator Pythagorean normal set Complex Diophantine set Multiple-attribute decision-making |
| title | Complex Diophantine interval-valued Pythagorean normal set for decision-making processes |
| title_full | Complex Diophantine interval-valued Pythagorean normal set for decision-making processes |
| title_fullStr | Complex Diophantine interval-valued Pythagorean normal set for decision-making processes |
| title_full_unstemmed | Complex Diophantine interval-valued Pythagorean normal set for decision-making processes |
| title_short | Complex Diophantine interval-valued Pythagorean normal set for decision-making processes |
| title_sort | complex diophantine interval valued pythagorean normal set for decision making processes |
| topic | Aggregating operator Pythagorean normal set Complex Diophantine set Multiple-attribute decision-making |
| url | https://doi.org/10.1038/s41598-024-82532-2 |
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