W-АЛГЕБРА В ЗАДАЧАХ НЕЧЕТКОЙ ЛИНЕЙНОЙ РЕГРЕССИИ  С ЧЕТКИМИ ПАРАМЕТРАМИ

Михаил Григорьевич Матвеев; Елена Николаевна Свиридова

doi:10.17308/sait/1995-5499/2025/4/132-144

Authors

Mikhail G. Matveev Voronezh State University https://orcid.org/0000-0002-6528-6420 (unauthenticated)
Elena N. Sviridova Air Force Academy named after Professor N. E. Zhukovsky and Yu. A. Gagarin https://orcid.org/0009-0009-3950-3370 (unauthenticated)

DOI:

https://doi.org/10.17308/sait/1995-5499/2025/4/132-144

Keywords:

fuzzy linear regression, W-algebra, computational complexity, least squares method, triangular fuzzy numbers, a-cuts, solution stability

Abstract

This paper investigates the application of W-algebra of fuzzy numbers for constructing fuzzy linear regression (FLR) models. The primary objective of the work is to overcome the fundamental limitations inherent in traditional methods based on a-cuts, namely: high com putational complexity, solution instability, and stringent requirements on the shape of fuzzy data membership functions (symmetry, non-negativity of spreads). The proposed approach utilizes the algebraic structure of W-algebra, which operates with two-component triangular numbers (w-numbers). A key advantage is that arithmetic operations on such numbers are performed independently on their left and right components. This allows the optimization problem to be reduced to a classical least squares method (LSM) formulation. The paper proves that minimizing the integral metric between the modelled and observed fuzzy values is equivalent to minimizing the distance between the values of these functions at the midpoint (a = 0,5). This transformation converts the original complex problem into a search for crisp regression coefficients by minimizing a standard quadratic function. A comparative analysis with well-known methods on synthetic data demonstrates that the method based on W-algebra provides comparable model quality (as assessed by RMSE and Fuzzy Determination Coefficient metrics). Crucially, it achieves this with a computational complexity that is reduced. Furthermore, the method is devoid of the solution instability problem characteristic of algorithms operating with a-cuts.

Author Biographies

Mikhail G. Matveev, Voronezh State University

PhD, Professor, Head of the Department of Information Technologies in Management
Elena N. Sviridova, Air Force Academy named after Professor N. E. Zhukovsky and Yu. A. Gagarin

PhD, Associate Professor, Associate Professor of Department of Mathematics

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