Multi attribute decision-making algorithms using Hamacher Choquet-integral operators with complex intuitionistic fuzzy information
The Choquet integral is a fuzzy measure that serves as an effective aggregation operator for combining a limited number of components into a single set. In 1978, Hamacher introduced the Hamacher t-norm and t-conorm, an expanded version of algebraic t-norms. In this article, we present the aggregatio...
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| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241700 |
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| author | Tehreem Harish Garg Kinza Ayaz Walid Emam |
| author_facet | Tehreem Harish Garg Kinza Ayaz Walid Emam |
| author_sort | Tehreem |
| collection | DOAJ |
| description | The Choquet integral is a fuzzy measure that serves as an effective aggregation operator for combining a limited number of components into a single set. In 1978, Hamacher introduced the Hamacher t-norm and t-conorm, an expanded version of algebraic t-norms. In this article, we present the aggregation operators for the Choquet integral that utilize the Hamacher t-norms to handle the theory of complex intuitionistic fuzzy values. These operators include the complex intuitionistic fuzzy Hamacher Choquet integral averaging and geometric operators. Additionally, an analysis is conducted on the attributes and special situations of the suggested methodologies. In addition, a novel approach is presented, utilizing newly developed operators for solving multi-attribute decision-making issues with complex intuitionistic fuzzy values. The operational stages of this strategy are thoroughly presented. Finally, we conducted a comprehensive comparison between the proposed methodology and existing approaches, using illustrative examples to validate the effectiveness and demonstrate the advantages of the proposed methods. |
| format | Article |
| id | doaj-art-b1b14676a4cc43b1a9bc8ad9d0c1eefc |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-b1b14676a4cc43b1a9bc8ad9d0c1eefc2025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912358603588410.3934/math.20241700Multi attribute decision-making algorithms using Hamacher Choquet-integral operators with complex intuitionistic fuzzy informationTehreem0Harish Garg1Kinza Ayaz2Walid Emam3Department of Mathematics, Faculty of Basic and Applied Sciences, Air University PAF Complex E-9, Islamabad, 44000, PakistanDepartment of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), Patiala 147004, Punjab, IndiaDepartment of Physics, Faculty of Basic and Applied Sciences, Air University PAF Complex E-9, Islamabad, 44000, PakistanDepartment of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaThe Choquet integral is a fuzzy measure that serves as an effective aggregation operator for combining a limited number of components into a single set. In 1978, Hamacher introduced the Hamacher t-norm and t-conorm, an expanded version of algebraic t-norms. In this article, we present the aggregation operators for the Choquet integral that utilize the Hamacher t-norms to handle the theory of complex intuitionistic fuzzy values. These operators include the complex intuitionistic fuzzy Hamacher Choquet integral averaging and geometric operators. Additionally, an analysis is conducted on the attributes and special situations of the suggested methodologies. In addition, a novel approach is presented, utilizing newly developed operators for solving multi-attribute decision-making issues with complex intuitionistic fuzzy values. The operational stages of this strategy are thoroughly presented. Finally, we conducted a comprehensive comparison between the proposed methodology and existing approaches, using illustrative examples to validate the effectiveness and demonstrate the advantages of the proposed methods.https://www.aimspress.com/article/doi/10.3934/math.20241700choquet-integralhamacher t-norms and t-conormscomplex intuitionistic fuzzy setsaverage aggregation operatorsgeometric aggregation operatorsdecision-making methods |
| spellingShingle | Tehreem Harish Garg Kinza Ayaz Walid Emam Multi attribute decision-making algorithms using Hamacher Choquet-integral operators with complex intuitionistic fuzzy information AIMS Mathematics choquet-integral hamacher t-norms and t-conorms complex intuitionistic fuzzy sets average aggregation operators geometric aggregation operators decision-making methods |
| title | Multi attribute decision-making algorithms using Hamacher Choquet-integral operators with complex intuitionistic fuzzy information |
| title_full | Multi attribute decision-making algorithms using Hamacher Choquet-integral operators with complex intuitionistic fuzzy information |
| title_fullStr | Multi attribute decision-making algorithms using Hamacher Choquet-integral operators with complex intuitionistic fuzzy information |
| title_full_unstemmed | Multi attribute decision-making algorithms using Hamacher Choquet-integral operators with complex intuitionistic fuzzy information |
| title_short | Multi attribute decision-making algorithms using Hamacher Choquet-integral operators with complex intuitionistic fuzzy information |
| title_sort | multi attribute decision making algorithms using hamacher choquet integral operators with complex intuitionistic fuzzy information |
| topic | choquet-integral hamacher t-norms and t-conorms complex intuitionistic fuzzy sets average aggregation operators geometric aggregation operators decision-making methods |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241700 |
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