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An Approach to the Total Least Squares Method for Symmetric Triangular Fuzzy Numbers

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  • Marius Giuclea

    (Department of Applied Mathematics, Bucharest University of Economic Studies, Calea Dorobanţi, 15-17, 010552 Bucharest, Romania
    Institute of Solid Mechanics, Romanian Academy, 15 Constantin Mille, 010141 Bucharest, Romania)

  • Costin-Ciprian Popescu

    (Department of Applied Mathematics, Bucharest University of Economic Studies, Calea Dorobanţi, 15-17, 010552 Bucharest, Romania)

Abstract

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.

Suggested Citation

  • Marius Giuclea & Costin-Ciprian Popescu, 2025. "An Approach to the Total Least Squares Method for Symmetric Triangular Fuzzy Numbers," Mathematics, MDPI, vol. 13(8), pages 1-49, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:8:p:1224-:d:1630383
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    References listed on IDEAS

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    1. Coppi, Renato & D'Urso, Pierpaolo & Giordani, Paolo & Santoro, Adriana, 2006. "Least squares estimation of a linear regression model with LR fuzzy response," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 267-286, November.
    2. Berlin Wu & Chin Feng Hung, 2016. "Innovative Correlation Coefficient Measurement with Fuzzy Data," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-11, May.
    3. Ebubekir Karabacak & Hüseyin Ali Kutlu, 2024. "Evaluating the Efficiencies of Logistics Centers with Fuzzy Logic: The Case of Turkey," Sustainability, MDPI, vol. 16(1), pages 1-25, January.
    4. Ramos, Jose A., 2007. "Applications of TLS and related methods in the environmental sciences," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 1234-1267, October.
    5. Hongmei Shi & Xingbo Zhang & Yuzhen Gao & Shuai Wang & Yufu Ning, 2023. "Robust Total Least Squares Estimation Method for Uncertain Linear Regression Model," Mathematics, MDPI, vol. 11(20), pages 1-9, October.
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