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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Main Authors: Marius Giuclea, Costin-Ciprian Popescu
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/13/8/1224
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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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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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