An $\alpha$-Parametric LU Decomposition Framework for Fully Fuzzy Linear Fractional Programming with Industrial Applications

Kandasamy Ganesan; Ganesan Anitha

doi:10.32323/ujma.1883276

An $\alpha$-Parametric LU Decomposition Framework for Fully Fuzzy Linear Fractional Programming with Industrial Applications

Abstract

The work addresses the Fully Fuzzy Linear Fractional Programming Problem (FFLFPP) where the objective functions and the constraints are expressed by fuzzy parameters in the form of Triangular Fuzzy Numbers (TFNs) in such a way that the defuzzification to crisp values is not necessary. A hybrid computational framework is proposed to cope with the inherent uncertainty and nonlinearity. The $\alpha$-cut representation is used to convert the fuzzy coefficients to the corresponding parametric forms, while the structural consistency of the original model is maintained. This transformation enables us to convert the FFLFPP into an equivalent Fully Fuzzy Linear Programming (FFLP) model. The obtained model is solved using the LU decomposition method. Also, a theorem for the parametric LU factorization of TFN's is established, revealing the existence conditions and the general form of the solutions. Numerical examples from real life applications demonstrate the efficiency and practical applicability of the proposed approach.

Keywords

Fully fuzzy linear fractional programming, Triangular fuzzy numbers, $\alpha$-cut representation, Conversion technique, LU decomposition

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Details

Primary Language

English

Subjects

Mathematical Optimisation

Journal Section

Research Article

Authors

Kandasamy Ganesan ^*
0000-0002-4532-0222
India

Ganesan Anitha
0009-0004-9233-8451
India

Early Pub Date

June 20, 2026

Publication Date

June 26, 2026

Submission Date

February 6, 2026

Acceptance Date

May 24, 2026

Published in Issue

Year 2026 Volume: 9 Number: 2

DOI

https://doi.org/10.32323/ujma.1883276

IZ

https://izlik.org/JA55CY44EM

APA

Ganesan, K., & Anitha, G. (2026). An $\alpha$-Parametric LU Decomposition Framework for Fully Fuzzy Linear Fractional Programming with Industrial Applications. Universal Journal of Mathematics and Applications, 9(2), 109-123. https://doi.org/10.32323/ujma.1883276

AMA

1.Ganesan K, Anitha G. An $\alpha$-Parametric LU Decomposition Framework for Fully Fuzzy Linear Fractional Programming with Industrial Applications. Univ. J. Math. Appl. 2026;9(2):109-123. doi:10.32323/ujma.1883276

Chicago

Ganesan, Kandasamy, and Ganesan Anitha. 2026. “An $\alpha$-Parametric LU Decomposition Framework for Fully Fuzzy Linear Fractional Programming With Industrial Applications”. Universal Journal of Mathematics and Applications 9 (2): 109-23. https://doi.org/10.32323/ujma.1883276.

EndNote

Ganesan K, Anitha G (June 1, 2026) An $\alpha$-Parametric LU Decomposition Framework for Fully Fuzzy Linear Fractional Programming with Industrial Applications. Universal Journal of Mathematics and Applications 9 2 109–123.

IEEE

[1]K. Ganesan and G. Anitha, “An $\alpha$-Parametric LU Decomposition Framework for Fully Fuzzy Linear Fractional Programming with Industrial Applications”, Univ. J. Math. Appl., vol. 9, no. 2, pp. 109–123, June 2026, doi: 10.32323/ujma.1883276.

ISNAD

Ganesan, Kandasamy - Anitha, Ganesan. “An $\alpha$-Parametric LU Decomposition Framework for Fully Fuzzy Linear Fractional Programming With Industrial Applications”. Universal Journal of Mathematics and Applications 9/2 (June 1, 2026): 109-123. https://doi.org/10.32323/ujma.1883276.

JAMA

1.Ganesan K, Anitha G. An $\alpha$-Parametric LU Decomposition Framework for Fully Fuzzy Linear Fractional Programming with Industrial Applications. Univ. J. Math. Appl. 2026;9:109–123.

MLA

Ganesan, Kandasamy, and Ganesan Anitha. “An $\alpha$-Parametric LU Decomposition Framework for Fully Fuzzy Linear Fractional Programming With Industrial Applications”. Universal Journal of Mathematics and Applications, vol. 9, no. 2, June 2026, pp. 109-23, doi:10.32323/ujma.1883276.

Vancouver

1.Kandasamy Ganesan, Ganesan Anitha. An $\alpha$-Parametric LU Decomposition Framework for Fully Fuzzy Linear Fractional Programming with Industrial Applications. Univ. J. Math. Appl. 2026 Jun. 1;9(2):109-23. doi:10.32323/ujma.1883276