Heronian Mean Operators Based on Novel Complex Linear Diophantine Uncertain Linguistic Variables and Their Applications in Multi-Attribute Decision Making
In this manuscript, we combine the notion of linear Diophantine fuzzy set (LDFS), uncertain linguistic set (ULS), and complex fuzzy set (CFS) to elaborate the notion of complex linear Diophantine uncertain linguistic set (CLDULS). CLDULS refers to truth, falsity, reference parameters, and their unce...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/21/2730 |
| _version_ | 1797512092158263296 |
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| author | Zeeshan Ali Tahir Mahmood Gustavo Santos-García |
| author_facet | Zeeshan Ali Tahir Mahmood Gustavo Santos-García |
| author_sort | Zeeshan Ali |
| collection | DOAJ |
| description | In this manuscript, we combine the notion of linear Diophantine fuzzy set (LDFS), uncertain linguistic set (ULS), and complex fuzzy set (CFS) to elaborate the notion of complex linear Diophantine uncertain linguistic set (CLDULS). CLDULS refers to truth, falsity, reference parameters, and their uncertain linguistic terms to handle problematic and challenging data in factual life impasses. By using the elaborated CLDULSs, some operational laws are also settled. Furthermore, by using the power Einstein (PE) aggregation operators based on CLDULS: the complex linear Diophantine uncertain linguistic PE averaging (CLDULPEA), complex linear Diophantine uncertain linguistic PE weighted averaging (CLDULPEWA), complex linear Diophantine uncertain linguistic PE Geometric (CLDULPEG), and complex linear Diophantine uncertain linguistic PE weighted geometric (CLDULPEWG) operators, and their useful results are elaborated with the help of some remarkable cases. Additionally, by utilizing the expounded works dependent on CLDULS, I propose a multi-attribute decision-making (MADM) issue. To decide the quality of the expounded works, some mathematical models are outlined. Finally, the incomparability and relative examination of the expounded approaches with the assistance of graphical articulations are evolved. |
| first_indexed | 2024-03-10T05:57:01Z |
| format | Article |
| id | doaj.art-95b0d53a10854ccfac3deab5cdf9998d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T05:57:01Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-95b0d53a10854ccfac3deab5cdf9998d2023-11-22T21:18:01ZengMDPI AGMathematics2227-73902021-10-01921273010.3390/math9212730Heronian Mean Operators Based on Novel Complex Linear Diophantine Uncertain Linguistic Variables and Their Applications in Multi-Attribute Decision MakingZeeshan Ali0Tahir Mahmood1Gustavo Santos-García2Department of Mathematics & Statistics, International Islamic University Islamabad, Islamabad 44000, PakistanDepartment of Mathematics & Statistics, International Islamic University Islamabad, Islamabad 44000, PakistanInstituto Multidisciplinar de Empresa (IME), University of Salamanca, 37007 Salamanca, SpainIn this manuscript, we combine the notion of linear Diophantine fuzzy set (LDFS), uncertain linguistic set (ULS), and complex fuzzy set (CFS) to elaborate the notion of complex linear Diophantine uncertain linguistic set (CLDULS). CLDULS refers to truth, falsity, reference parameters, and their uncertain linguistic terms to handle problematic and challenging data in factual life impasses. By using the elaborated CLDULSs, some operational laws are also settled. Furthermore, by using the power Einstein (PE) aggregation operators based on CLDULS: the complex linear Diophantine uncertain linguistic PE averaging (CLDULPEA), complex linear Diophantine uncertain linguistic PE weighted averaging (CLDULPEWA), complex linear Diophantine uncertain linguistic PE Geometric (CLDULPEG), and complex linear Diophantine uncertain linguistic PE weighted geometric (CLDULPEWG) operators, and their useful results are elaborated with the help of some remarkable cases. Additionally, by utilizing the expounded works dependent on CLDULS, I propose a multi-attribute decision-making (MADM) issue. To decide the quality of the expounded works, some mathematical models are outlined. Finally, the incomparability and relative examination of the expounded approaches with the assistance of graphical articulations are evolved.https://www.mdpi.com/2227-7390/9/21/2730complex linear Diophantine uncertain linguistic setspowered Einstein aggregation operatorsmulti-attribute decision-making methods |
| spellingShingle | Zeeshan Ali Tahir Mahmood Gustavo Santos-García Heronian Mean Operators Based on Novel Complex Linear Diophantine Uncertain Linguistic Variables and Their Applications in Multi-Attribute Decision Making Mathematics complex linear Diophantine uncertain linguistic sets powered Einstein aggregation operators multi-attribute decision-making methods |
| title | Heronian Mean Operators Based on Novel Complex Linear Diophantine Uncertain Linguistic Variables and Their Applications in Multi-Attribute Decision Making |
| title_full | Heronian Mean Operators Based on Novel Complex Linear Diophantine Uncertain Linguistic Variables and Their Applications in Multi-Attribute Decision Making |
| title_fullStr | Heronian Mean Operators Based on Novel Complex Linear Diophantine Uncertain Linguistic Variables and Their Applications in Multi-Attribute Decision Making |
| title_full_unstemmed | Heronian Mean Operators Based on Novel Complex Linear Diophantine Uncertain Linguistic Variables and Their Applications in Multi-Attribute Decision Making |
| title_short | Heronian Mean Operators Based on Novel Complex Linear Diophantine Uncertain Linguistic Variables and Their Applications in Multi-Attribute Decision Making |
| title_sort | heronian mean operators based on novel complex linear diophantine uncertain linguistic variables and their applications in multi attribute decision making |
| topic | complex linear Diophantine uncertain linguistic sets powered Einstein aggregation operators multi-attribute decision-making methods |
| url | https://www.mdpi.com/2227-7390/9/21/2730 |
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