A Novel Approach for Solving the Triangular Fuzzy Neutrosophic Assignment Problem

Abstract

The assignment problem (AP) is a fundamental challenge in linear programming and operations research focused on optimizing assignments to minimize costs or maximize profits. This study extends the traditional AP to address uncertainties and ambiguities through the neutrosophic assignment problem (NAP). Further advancing this concept, the triangular fuzzy neutrosophic assignment problem (TFNAP) is introduced, utilizing triangular fuzzy neutrosophic numbers (TFNNs) to represent fuzziness and neutrosophy, thus offering a more comprehensive depiction of uncertainty and indeterminacy. The primary aim of this research is to identify the optimal assignment that either minimizes cost or maximizes profit within the TFNAP framework, a task known for its computational complexity. The TFNAP is represented through a triangular fuzzy neutrosophic assignment matrix (TFNAM), which employs TFNNs as its core elements. This study develops and refines algorithms tailored to address these complexities, ensuring originality through a stepwise procedure that simplifies computations in a neutrosophic manner. The methodology includes resolving the problem using a neutrosophic approach and incorporating a score function to convert triangular fuzzy neutrosophic values to their equivalent crisp numbers for comparative purposes. The proposed method’s effectiveness is validated through its application to real-world problems, with the results compared against previously established solutions. The findings demonstrate that the TFNAP framework provides more accurate and insightful outcomes in dealing with uncertainties compared to traditional methods. This study introduces significant innovations in handling ambiguity and indeterminacy in assignment problems, offering a robust tool for optimization in complex, uncertain environments. Conclusively, the developed approach not only enhances the understanding of neutrosophic assignments but also presents a practical solution for real-world applications.