Extensions of Dombi Aggregation Operators for Decision Making under m-Polar Fuzzy Information
An m-polar fuzzy set is a powerful mathematical model to analyze multipolar, multiattribute, and multi-index data. The m-polar fuzzy sets have appeared as a useful tool to portray uncertainty in multiattribute decision making. The purpose of this article is to analyze the aggregation operators under...
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/4739567 |
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| author | Muhammad Akram Naveed Yaqoob Ghous Ali Wathek Chammam |
| author_facet | Muhammad Akram Naveed Yaqoob Ghous Ali Wathek Chammam |
| author_sort | Muhammad Akram |
| collection | DOAJ |
| description | An m-polar fuzzy set is a powerful mathematical model to analyze multipolar, multiattribute, and multi-index data. The m-polar fuzzy sets have appeared as a useful tool to portray uncertainty in multiattribute decision making. The purpose of this article is to analyze the aggregation operators under the m-polar fuzzy environment with the help of Dombi norm operations. In this article, we develop some averaging and geometric aggregation operators using Dombi t-norm and t-conorm to handle uncertainty in m-polar fuzzy (mF, henceforth) information, which are mF Dombi weighted averaging (mFDWA) operator, mF Dombi ordered weighted averaging (mFDOWA) operator, mF Dombi hybrid averaging (mFDHA) operator, mF Dombi weighted geometric (mFDWG) operator, mF Dombi weighted ordered geometric operator, and mF Dombi hybrid geometric (mFDHG) operator. We investigate properties, namely, idempotency, monotonicity, and boundedness, for the proposed operators. Moreover, we give an algorithm to solve multicriteria decision-making issues which involve mF information with mFDWA and mFDWG operators. To prove the validity and feasibility of the proposed model, we solve two numerical examples with our proposed models and give comparison with mF-ELECTRE-I approach (Akram et al. 2019) and mF Hamacher aggregation operators (Waseem et al. 2019). Finally, we check the effectiveness of the developed operators by a validity test. |
| format | Article |
| id | doaj-art-5c2bafcee4d941ce9d2aabbb87f87e7a |
| institution | OA Journals |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
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| spelling | doaj-art-5c2bafcee4d941ce9d2aabbb87f87e7a2025-08-20T02:05:42ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/47395674739567Extensions of Dombi Aggregation Operators for Decision Making under m-Polar Fuzzy InformationMuhammad Akram0Naveed Yaqoob1Ghous Ali2Wathek Chammam3Department of Mathematics, University of the Punjab, New Campus, Lahore, PakistanDepartment of Mathematics and Statistics, Riphah International University, I-14, Islamabad, PakistanDepartment of Mathematics, University of the Punjab, New Campus, Lahore, PakistanDepartment of Mathematics, College of Science, Al Zulfi, Majmaah University, P.O. Box 66, Al-Majmaah 11952, Saudi ArabiaAn m-polar fuzzy set is a powerful mathematical model to analyze multipolar, multiattribute, and multi-index data. The m-polar fuzzy sets have appeared as a useful tool to portray uncertainty in multiattribute decision making. The purpose of this article is to analyze the aggregation operators under the m-polar fuzzy environment with the help of Dombi norm operations. In this article, we develop some averaging and geometric aggregation operators using Dombi t-norm and t-conorm to handle uncertainty in m-polar fuzzy (mF, henceforth) information, which are mF Dombi weighted averaging (mFDWA) operator, mF Dombi ordered weighted averaging (mFDOWA) operator, mF Dombi hybrid averaging (mFDHA) operator, mF Dombi weighted geometric (mFDWG) operator, mF Dombi weighted ordered geometric operator, and mF Dombi hybrid geometric (mFDHG) operator. We investigate properties, namely, idempotency, monotonicity, and boundedness, for the proposed operators. Moreover, we give an algorithm to solve multicriteria decision-making issues which involve mF information with mFDWA and mFDWG operators. To prove the validity and feasibility of the proposed model, we solve two numerical examples with our proposed models and give comparison with mF-ELECTRE-I approach (Akram et al. 2019) and mF Hamacher aggregation operators (Waseem et al. 2019). Finally, we check the effectiveness of the developed operators by a validity test.http://dx.doi.org/10.1155/2020/4739567 |
| spellingShingle | Muhammad Akram Naveed Yaqoob Ghous Ali Wathek Chammam Extensions of Dombi Aggregation Operators for Decision Making under m-Polar Fuzzy Information Journal of Mathematics |
| title | Extensions of Dombi Aggregation Operators for Decision Making under m-Polar Fuzzy Information |
| title_full | Extensions of Dombi Aggregation Operators for Decision Making under m-Polar Fuzzy Information |
| title_fullStr | Extensions of Dombi Aggregation Operators for Decision Making under m-Polar Fuzzy Information |
| title_full_unstemmed | Extensions of Dombi Aggregation Operators for Decision Making under m-Polar Fuzzy Information |
| title_short | Extensions of Dombi Aggregation Operators for Decision Making under m-Polar Fuzzy Information |
| title_sort | extensions of dombi aggregation operators for decision making under m polar fuzzy information |
| url | http://dx.doi.org/10.1155/2020/4739567 |
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