A Theoretical Development of Cubic Pythagorean Fuzzy Soft Set with Its Application in Multi-Attribute Decision Making
Scientific progression has allowed researchers to develop novel and innovative ways to deal with uncertainty in data, allowing for the development of more precise and accurate data representation models. This paper aims to extend an already reported concept of Cubic Pythagorean fuzzy set to Cubic Py...
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| Format: | Article |
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MDPI AG
2022-12-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/12/2639 |
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| author | Muhammad Saeed Muhammad Haris Saeed Rimsha Shafaqat Salvatore Sessa Umar Ishtiaq Ferdinando di Martino |
| author_facet | Muhammad Saeed Muhammad Haris Saeed Rimsha Shafaqat Salvatore Sessa Umar Ishtiaq Ferdinando di Martino |
| author_sort | Muhammad Saeed |
| collection | DOAJ |
| description | Scientific progression has allowed researchers to develop novel and innovative ways to deal with uncertainty in data, allowing for the development of more precise and accurate data representation models. This paper aims to extend an already reported concept of Cubic Pythagorean fuzzy set to Cubic Pythagorean Fuzzy Soft Set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>C</mi><mrow><mi>P</mi><mi>F</mi><mi>S</mi><mi>s</mi></mrow></msub><mo>)</mo></mrow></semantics></math></inline-formula> as it incorporates both interval-valued Pythagorean fuzzy sets (IVPFS) and Pythagorean fuzzy sets (PFS) at the same time, providing a more targeted approach to deal with uncertainty. This hybrid structure can better handle data in comparison to the ones in the literature by having the characteristics of PFS and soft sets, leading to a more targeted approach to handle attributes in decision-making studies. In this study, we defined various internals and externals of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>C</mi><mrow><mi>P</mi><mi>F</mi><mi>S</mi><mi>s</mi></mrow></msub></semantics></math></inline-formula>, set operators, aggregation operators, and developed an algorithm based on distance measures for (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>C</mi><mrow><mi>P</mi><mi>F</mi><mi>S</mi><mi>s</mi></mrow></msub></semantics></math></inline-formula>), which are applied in a disease diagnostic decision-making problem. |
| first_indexed | 2024-03-09T15:48:12Z |
| format | Article |
| id | doaj.art-efa71447bbd349f789d5c5e9409dcef1 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T15:48:12Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-efa71447bbd349f789d5c5e9409dcef12023-11-24T18:20:33ZengMDPI AGSymmetry2073-89942022-12-011412263910.3390/sym14122639A Theoretical Development of Cubic Pythagorean Fuzzy Soft Set with Its Application in Multi-Attribute Decision MakingMuhammad Saeed0Muhammad Haris Saeed1Rimsha Shafaqat2Salvatore Sessa3Umar Ishtiaq4Ferdinando di Martino5Department of Mathematics, University of Management and Technology, Lahore 54000, PakistanDepartment of Chemistry, University of Management and Technology, Lahore 54000, PakistanDepartment of Mathematics, University of Management and Technology, Lahore 54000, PakistanDipartimento di Architettura, Università Dinapoli Federico II, Via Toledo 403, 80121 Napoli, ItalyOffice of Research, Innovation and Commercialization, University of Management and Technology, Lahore 54000, PakistanDipartimento di Architettura, Università Dinapoli Federico II, Via Toledo 403, 80121 Napoli, ItalyScientific progression has allowed researchers to develop novel and innovative ways to deal with uncertainty in data, allowing for the development of more precise and accurate data representation models. This paper aims to extend an already reported concept of Cubic Pythagorean fuzzy set to Cubic Pythagorean Fuzzy Soft Set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>C</mi><mrow><mi>P</mi><mi>F</mi><mi>S</mi><mi>s</mi></mrow></msub><mo>)</mo></mrow></semantics></math></inline-formula> as it incorporates both interval-valued Pythagorean fuzzy sets (IVPFS) and Pythagorean fuzzy sets (PFS) at the same time, providing a more targeted approach to deal with uncertainty. This hybrid structure can better handle data in comparison to the ones in the literature by having the characteristics of PFS and soft sets, leading to a more targeted approach to handle attributes in decision-making studies. In this study, we defined various internals and externals of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>C</mi><mrow><mi>P</mi><mi>F</mi><mi>S</mi><mi>s</mi></mrow></msub></semantics></math></inline-formula>, set operators, aggregation operators, and developed an algorithm based on distance measures for (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>C</mi><mrow><mi>P</mi><mi>F</mi><mi>S</mi><mi>s</mi></mrow></msub></semantics></math></inline-formula>), which are applied in a disease diagnostic decision-making problem.https://www.mdpi.com/2073-8994/14/12/2639fuzzy set theorysoft setdecision makingdistance measuressimilarity measures |
| spellingShingle | Muhammad Saeed Muhammad Haris Saeed Rimsha Shafaqat Salvatore Sessa Umar Ishtiaq Ferdinando di Martino A Theoretical Development of Cubic Pythagorean Fuzzy Soft Set with Its Application in Multi-Attribute Decision Making Symmetry fuzzy set theory soft set decision making distance measures similarity measures |
| title | A Theoretical Development of Cubic Pythagorean Fuzzy Soft Set with Its Application in Multi-Attribute Decision Making |
| title_full | A Theoretical Development of Cubic Pythagorean Fuzzy Soft Set with Its Application in Multi-Attribute Decision Making |
| title_fullStr | A Theoretical Development of Cubic Pythagorean Fuzzy Soft Set with Its Application in Multi-Attribute Decision Making |
| title_full_unstemmed | A Theoretical Development of Cubic Pythagorean Fuzzy Soft Set with Its Application in Multi-Attribute Decision Making |
| title_short | A Theoretical Development of Cubic Pythagorean Fuzzy Soft Set with Its Application in Multi-Attribute Decision Making |
| title_sort | theoretical development of cubic pythagorean fuzzy soft set with its application in multi attribute decision making |
| topic | fuzzy set theory soft set decision making distance measures similarity measures |
| url | https://www.mdpi.com/2073-8994/14/12/2639 |
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