DOI: 10.32323/ujma.1883276 ISSN: 2619-9653

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

Kandasamy Ganesan, G Anitha
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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.

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