Fermatean Cubic Fuzzy Aggregation Operators and Their Application in Multiattribute Decision-Making Problems
The purpose of aggregation methods is to convert a list of objects of a set into a single object of the same set usually by an n-arry function, so-called aggregation operator. The key features of this work are the aggregation operators, because they are based on a novel set called Fermatean cubic fu...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/3664302 |
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| author | Muhammad Riaz Aurang Zeb Fawad Ali Muhammad Naeem Sama Arjika |
| author_facet | Muhammad Riaz Aurang Zeb Fawad Ali Muhammad Naeem Sama Arjika |
| author_sort | Muhammad Riaz |
| collection | DOAJ |
| description | The purpose of aggregation methods is to convert a list of objects of a set into a single object of the same set usually by an n-arry function, so-called aggregation operator. The key features of this work are the aggregation operators, because they are based on a novel set called Fermatean cubic fuzzy set (F-CFS). F-CFS has greater spatial scope and can deal with more ambiguous situations where other fuzzy set extensions fail to support them. For this purpose, the notion of F-CFS is defined. F-CFS is the transformation of intuitionistic cubic fuzzy set (I-CFS), Pythagorean cubic fuzzy set (P-CFS), interval-valued cubic fuzzy set, and basic orthopair fuzzy set and is grounded on the constraint that “the cube of the supremum of membership plus nonmembership degree is ≤1”. We have analyzed some properties of Fermatean cubic fuzzy numbers (F-CFNs) as they are the alteration of basic properties of I-CFS and P-CFS. We also have defined the score and deviation degrees of F-CFNs. Moreover, the distance measuring function between two F-CFNs is defined which shows the space between two F-CFNs. Based on this notion, the aggregation operators namely Fermatean cubic fuzzy-weighted averaging operator (F-CFWA), Fermatean cubic fuzzy-weighted geometric operator (F-CFWG), Fermatean cubic fuzzy-ordered-weighted averaging operator (F-CFOWA), and Fermatean cubic fuzzy-ordered-weighted geometric operator (F-CFOWG) are developed. Furthermore, the notion is applied to multiattribute decision-making (MADM) problem in which we presented our objectives in the form of F-CFNs to show the effectiveness of the newly developed strategy. |
| format | Article |
| id | doaj-art-83638d4c42034bb1bf5876ff8d60d70e |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-83638d4c42034bb1bf5876ff8d60d70e2025-02-03T05:57:25ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/3664302Fermatean Cubic Fuzzy Aggregation Operators and Their Application in Multiattribute Decision-Making ProblemsMuhammad Riaz0Aurang Zeb1Fawad Ali2Muhammad Naeem3Sama Arjika4Department of MathematicsSchool of Mathematics and StatisticsInstitute of Numerical SciencesDepartment of MathematicsDepartment of Mathematics and InformaticsThe purpose of aggregation methods is to convert a list of objects of a set into a single object of the same set usually by an n-arry function, so-called aggregation operator. The key features of this work are the aggregation operators, because they are based on a novel set called Fermatean cubic fuzzy set (F-CFS). F-CFS has greater spatial scope and can deal with more ambiguous situations where other fuzzy set extensions fail to support them. For this purpose, the notion of F-CFS is defined. F-CFS is the transformation of intuitionistic cubic fuzzy set (I-CFS), Pythagorean cubic fuzzy set (P-CFS), interval-valued cubic fuzzy set, and basic orthopair fuzzy set and is grounded on the constraint that “the cube of the supremum of membership plus nonmembership degree is ≤1”. We have analyzed some properties of Fermatean cubic fuzzy numbers (F-CFNs) as they are the alteration of basic properties of I-CFS and P-CFS. We also have defined the score and deviation degrees of F-CFNs. Moreover, the distance measuring function between two F-CFNs is defined which shows the space between two F-CFNs. Based on this notion, the aggregation operators namely Fermatean cubic fuzzy-weighted averaging operator (F-CFWA), Fermatean cubic fuzzy-weighted geometric operator (F-CFWG), Fermatean cubic fuzzy-ordered-weighted averaging operator (F-CFOWA), and Fermatean cubic fuzzy-ordered-weighted geometric operator (F-CFOWG) are developed. Furthermore, the notion is applied to multiattribute decision-making (MADM) problem in which we presented our objectives in the form of F-CFNs to show the effectiveness of the newly developed strategy.http://dx.doi.org/10.1155/2022/3664302 |
| spellingShingle | Muhammad Riaz Aurang Zeb Fawad Ali Muhammad Naeem Sama Arjika Fermatean Cubic Fuzzy Aggregation Operators and Their Application in Multiattribute Decision-Making Problems Journal of Function Spaces |
| title | Fermatean Cubic Fuzzy Aggregation Operators and Their Application in Multiattribute Decision-Making Problems |
| title_full | Fermatean Cubic Fuzzy Aggregation Operators and Their Application in Multiattribute Decision-Making Problems |
| title_fullStr | Fermatean Cubic Fuzzy Aggregation Operators and Their Application in Multiattribute Decision-Making Problems |
| title_full_unstemmed | Fermatean Cubic Fuzzy Aggregation Operators and Their Application in Multiattribute Decision-Making Problems |
| title_short | Fermatean Cubic Fuzzy Aggregation Operators and Their Application in Multiattribute Decision-Making Problems |
| title_sort | fermatean cubic fuzzy aggregation operators and their application in multiattribute decision making problems |
| url | http://dx.doi.org/10.1155/2022/3664302 |
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