ПРИМЕНЕНИЕ W-АЛГЕБРЫ ДЛЯ ПОСТРОЕНИЯ МОДЕЛЕЙ НЕЧЕТКОЙ ЛИНЕЙНОЙ РЕГРЕССИИ С НЕЧЕТКИМИ ПАРАМЕТРАМИ

Михаил Григорьевич Матвеев; Елена Николаевна Свиридова

doi:10.17308/sait/1995-5499/2026/1/156-166

Authors

Mikhail G. Matveev Voronezh State University
Elena N. Sviridova Air Force Academy named after Professor N. E. Zhukovsky and Yu. A. Gagarin

DOI:

https://doi.org/10.17308/sait/1995-5499/2026/1/156-166

Keywords:

fuzzy linear regression, W-algebra, fuzzy regression parameters, fuzzy numbers, membership functions

Abstract

This paper explores the application of W-algebra for constructing fuzzy linear regression models with fuzzy parameters. An analysis of existing fuzzy regression methods is conducted, including approaches based on fuzziness minimization and modifications of the least squares method. Their limitations are highlighted, such as sensitivity to outliers, unjustified growth of prediction interval widths, and strict data requirements. A novel approach based on W-algebra is proposed. This approach allows for the unification of operations on triangular fuzzy numbers by transforming the fuzzy regression problem into two independent ordinary linear regression problems for the left and right components of w-numbers. This significantly simplifies computations, enhances the robustness of estimates, and expands the class of data that can be processed, including non-symmetric fuzzy numbers. The results of numerical experiments on synthetic data demonstrate the advantages of the proposed method: a reduction in prediction fuzziness (AWCB metric) while simultaneously improving accuracy (MAE and MSE metrics) compared to classical methods. The approach also ensures computational efficiency, ease of implementation, and better interpretability of results, making it a promising tool for modeling under uncertainty.

Author Biographies

Mikhail G. Matveev, Voronezh State University

DSc in Technical Sciences, 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 in Physics and Mathematics, Associate Professor

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