A Novel Computational Approach for Linear Fractional Programming Problems in a Neutrosophic Environment

Abstract

This paper introduces a novel computational approach for solving neutrosophic linear fractional programming (NLFP) problems in which all objective coefficients, technological coefficients, resource values, and decision variables are represented by triangular neutrosophic numbers. The proposed method addresses the uncertainty, inconsistency, and indeterminacy inherent in real-world optimization problems by employing a neutrosophic environment characterized by truth, indeterminacy, and falsity membership degrees. A systematic transformation procedure is developed to reformulate the original NLFP model into an equivalent neutrosophic linear programming model through a parametric representation of the fractional objective function. Subsequently, a specialized ranking function is employed to convert triangular neutrosophic numbers into crisp values, enabling the formulation of a solvable linear programming model while preserving the essential uncertainty information contained in the original problem. The proposed methodology simplifies the computational procedure, reduces model complexity, and provides an efficient mechanism for obtaining optimal solutions under neutrosophic uncertainty. A detailed solution algorithm is presented, and a numerical example is provided to demonstrate the applicability and effectiveness of the proposed method. The obtained results are compared with several existing approaches from the literature, demonstrating that the proposed method produces reliable and competitive solutions while maintaining computational efficiency and simplicity. Overall, the findings confirm the suitability of the proposed methodology for solving NLFP problems and highlight its potential for extension to more complex optimization models under uncertain and indeterminate decision-making environments.