An Approach to the Total Least Squares Method for Symmetric Triangular Fuzzy Numbers
The total least squares method has a broad applicability in many fields. It is also useful in fuzzy data analysis. In this paper, we study the method of total least squares for fuzzy variables. The regression parameters are considered to be crisp. First, we find a formula for the distance between an...
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MDPI AG
2025-04-01
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| author | Marius Giuclea Costin-Ciprian Popescu |
| author_facet | Marius Giuclea Costin-Ciprian Popescu |
| author_sort | Marius Giuclea |
| collection | DOAJ |
| description | The total least squares method has a broad applicability in many fields. It is also useful in fuzzy data analysis. In this paper, we study the method of total least squares for fuzzy variables. The regression parameters are considered to be crisp. First, we find a formula for the distance between an arbitrary pair of triangular fuzzy numbers and the set described by the regression relation. Second, we develop a new approach to total least squares for data that are modeled as symmetric triangular fuzzy numbers. To illustrate the theoretical results obtained in the paper, some numerical examples are presented. |
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| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-c44e896d2f4d4bd7a0bcee29ce6ae0172025-08-20T02:28:15ZengMDPI AGMathematics2227-73902025-04-01138122410.3390/math13081224An Approach to the Total Least Squares Method for Symmetric Triangular Fuzzy NumbersMarius Giuclea0Costin-Ciprian Popescu1Department of Applied Mathematics, Bucharest University of Economic Studies, Calea Dorobanţi, 15-17, 010552 Bucharest, RomaniaDepartment of Applied Mathematics, Bucharest University of Economic Studies, Calea Dorobanţi, 15-17, 010552 Bucharest, RomaniaThe total least squares method has a broad applicability in many fields. It is also useful in fuzzy data analysis. In this paper, we study the method of total least squares for fuzzy variables. The regression parameters are considered to be crisp. First, we find a formula for the distance between an arbitrary pair of triangular fuzzy numbers and the set described by the regression relation. Second, we develop a new approach to total least squares for data that are modeled as symmetric triangular fuzzy numbers. To illustrate the theoretical results obtained in the paper, some numerical examples are presented.https://www.mdpi.com/2227-7390/13/8/1224regressiontotal least squaresfuzzy numberfuzzy regressiontriangular fuzzy numbersymmetric triangular fuzzy number |
| spellingShingle | Marius Giuclea Costin-Ciprian Popescu An Approach to the Total Least Squares Method for Symmetric Triangular Fuzzy Numbers Mathematics regression total least squares fuzzy number fuzzy regression triangular fuzzy number symmetric triangular fuzzy number |
| title | An Approach to the Total Least Squares Method for Symmetric Triangular Fuzzy Numbers |
| title_full | An Approach to the Total Least Squares Method for Symmetric Triangular Fuzzy Numbers |
| title_fullStr | An Approach to the Total Least Squares Method for Symmetric Triangular Fuzzy Numbers |
| title_full_unstemmed | An Approach to the Total Least Squares Method for Symmetric Triangular Fuzzy Numbers |
| title_short | An Approach to the Total Least Squares Method for Symmetric Triangular Fuzzy Numbers |
| title_sort | approach to the total least squares method for symmetric triangular fuzzy numbers |
| topic | regression total least squares fuzzy number fuzzy regression triangular fuzzy number symmetric triangular fuzzy number |
| url | https://www.mdpi.com/2227-7390/13/8/1224 |
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