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

Marius Giuclea () and Costin-Ciprian Popescu
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Marius Giuclea: Department of Applied Mathematics, Bucharest University of Economic Studies, Calea Dorobanţi, 15-17, 010552 Bucharest, Romania
Costin-Ciprian Popescu: Department of Applied Mathematics, Bucharest University of Economic Studies, Calea Dorobanţi, 15-17, 010552 Bucharest, Romania

Mathematics, 2025, vol. 13, issue 8, 1-49

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.

Keywords: regression; total least squares; fuzzy number; fuzzy regression; triangular fuzzy number; symmetric triangular fuzzy number (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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