An Innovative Approach for Solving Fully Triangular Q- Rung Orthopair Fuzzy Linear Fractional Optimization Problem

This paper addresses a nonlinear linear fractional programming (NLFP) problem characterized by parameter uncertainty. To effectively capture imprecision in the model, all coefficients in both the objective function and the constraints are represented using triangular q-rung orthopair fuzzy (q-ROF) numbers (q-ROFNs). The fuzzy formulation is then transformed into an equivalent crisp linear fractional programming model through the application of an appropriate score function. To solve the resulting deterministic model, a novel procedure based on the Fourier–Motzkin elimination technique is developed. The proposed method employs boundary analysis and provides a straightforward and computationally efficient alternative to classical approaches, such as the two-phase simplex method. Finally, a numerical example is included to illustrate the effectiveness and implementation steps of the proposed solution methodology, followed by concluding remarks.