Which Alternative for Solving Dual Fuzzy Nonlinear Equations Is More Precise?
To answer the question stated in the title, we present and compare two approaches: first, a standard approach for solving dual fuzzy nonlinear systems (DFN-systems) based on Newton’s method, which uses 2D FN representation and second, the new approach, based on multidimensional fuzzy arithmetic (MF-...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/9/1507 |
| _version_ | 1797554604268847104 |
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| author | Joanna Kołodziejczyk Andrzej Piegat Wojciech Sałabun |
| author_facet | Joanna Kołodziejczyk Andrzej Piegat Wojciech Sałabun |
| author_sort | Joanna Kołodziejczyk |
| collection | DOAJ |
| description | To answer the question stated in the title, we present and compare two approaches: first, a standard approach for solving dual fuzzy nonlinear systems (DFN-systems) based on Newton’s method, which uses 2D FN representation and second, the new approach, based on multidimensional fuzzy arithmetic (MF-arithmetic). We use a numerical example to explain how the proposed MF-arithmetic solves the DFN-system. To analyze results from the standard and the new approaches, we introduce an imprecision measure. We discuss the reasons why imprecision varies between both methods. The imprecision of the standard approach results (roots) is significant, which means that many possible values are excluded. |
| first_indexed | 2024-03-10T16:34:27Z |
| format | Article |
| id | doaj.art-f741b228f01c4e3dbd2a4a414b676ca5 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T16:34:27Z |
| publishDate | 2020-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-f741b228f01c4e3dbd2a4a414b676ca52023-11-20T12:36:31ZengMDPI AGMathematics2227-73902020-09-0189150710.3390/math8091507Which Alternative for Solving Dual Fuzzy Nonlinear Equations Is More Precise?Joanna Kołodziejczyk0Andrzej Piegat1Wojciech Sałabun2Research Team on Intelligent Decision Support Systems, Department of Artificial Intelligence Methods and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin ul. Żołnierska 49, 71-210 Szczecin, PolandResearch Team on Intelligent Decision Support Systems, Department of Artificial Intelligence Methods and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin ul. Żołnierska 49, 71-210 Szczecin, PolandResearch Team on Intelligent Decision Support Systems, Department of Artificial Intelligence Methods and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin ul. Żołnierska 49, 71-210 Szczecin, PolandTo answer the question stated in the title, we present and compare two approaches: first, a standard approach for solving dual fuzzy nonlinear systems (DFN-systems) based on Newton’s method, which uses 2D FN representation and second, the new approach, based on multidimensional fuzzy arithmetic (MF-arithmetic). We use a numerical example to explain how the proposed MF-arithmetic solves the DFN-system. To analyze results from the standard and the new approaches, we introduce an imprecision measure. We discuss the reasons why imprecision varies between both methods. The imprecision of the standard approach results (roots) is significant, which means that many possible values are excluded.https://www.mdpi.com/2227-7390/8/9/1507fuzzy nonlinear systemsfuzzy arithmeticfuzzy calculusmultidimensional fuzzy arithmeticRDM fuzzy arithmeticfuzzy parametric form |
| spellingShingle | Joanna Kołodziejczyk Andrzej Piegat Wojciech Sałabun Which Alternative for Solving Dual Fuzzy Nonlinear Equations Is More Precise? Mathematics fuzzy nonlinear systems fuzzy arithmetic fuzzy calculus multidimensional fuzzy arithmetic RDM fuzzy arithmetic fuzzy parametric form |
| title | Which Alternative for Solving Dual Fuzzy Nonlinear Equations Is More Precise? |
| title_full | Which Alternative for Solving Dual Fuzzy Nonlinear Equations Is More Precise? |
| title_fullStr | Which Alternative for Solving Dual Fuzzy Nonlinear Equations Is More Precise? |
| title_full_unstemmed | Which Alternative for Solving Dual Fuzzy Nonlinear Equations Is More Precise? |
| title_short | Which Alternative for Solving Dual Fuzzy Nonlinear Equations Is More Precise? |
| title_sort | which alternative for solving dual fuzzy nonlinear equations is more precise |
| topic | fuzzy nonlinear systems fuzzy arithmetic fuzzy calculus multidimensional fuzzy arithmetic RDM fuzzy arithmetic fuzzy parametric form |
| url | https://www.mdpi.com/2227-7390/8/9/1507 |
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