Picture Fuzzy Linear Programming Problems

This study introduces an advanced framework for picture fuzzy linear programming problems (PFLPP), deploying picture fuzzy numbers (PFNs) to articulate diverse parameters. Integral to this approach are the three cardinal membership functions: membership, neutral, and non-membership, each contributing distinctly to the formation of the PFLPP. Emphasis is placed on employing these degrees to formulate the PFLPP in its most unadulterated form. Furthermore, the research delineates a novel optimization model, tailored specifically for the resolution of the PFLPP. A meticulous case study, accompanied by a numerical example, is presented, demonstrating the efficacy and robustness of the proposed methodology. The study culminates in a comprehensive discussion of the findings, highlighting pivotal insights and delineating potential avenues for future inquiry. This exploration not only advances the theoretical underpinnings of picture fuzzy sets but also offers practical implications for the application of linear programming in complex decision-making scenarios.