Alternative method for solving the Single-Valued Triangular Fuzzy Neutrosophic Bi-Objective Assignment Problem

The Bi-Objective Assignment Problem (BOAP) is a well-known optimization challenge in linear programming and operations research. The aim of this study is to extend BOAP to handle inconsistencies and ambiguities through the Neutrosophic Bi-Objective Assignment Problem (NBOAP) and further refine it into the Single-Valued Triangular Fuzzy Neutrosophic Bi-Objective Assignment Problem (SVTFNBOAP). This work introduces Single-Valued Triangular Fuzzy Neutrosophic Numbers (SVTFNNs) to encapsulate fuzziness and neutrosophy, enabling optimal assignments that reduce costs or maximize profits. To address numerical complexity of SVTFNBOAP, represented by the Single-Valued Triangular Fuzzy Neutrosophic Bi-Objective Assignment Table (SVTFNBOAT), the study proposes a progressive strategy for simplifying calculations without sacrificing uniqueness. The findings validate the effectiveness of this method through real-world applications, where a score function is employed to convert SVTFNNs into crisp numbers for comparative analysis. The application of the proposed approach demonstrates its superiority over existing solutions, enhancing decision-making in complex optimization scenarios.