Abstract
The introduction of (p, q)-rung linear Diophantine fuzzy set into the field of fuzzy set theory is a significant advancement, providing a broader perspective to address complicated decision-making scenarios. Alongside, the preference ranking organization method for enrichment of evaluation (PROMETHEE) emerges as a widely recognized tool for tackling multi-criteria decision-making challenges. This study contributes theoretically to the decision-making field by integrating (p, q)-rung linear Diophantine fuzzy sets into the PROMETHEE framework, improving (p, q)-rung linear Diophantine fuzzy sets adaptability and efficiency in practical aspects, the proposed framework can effectively address various intricate decision-making challenges encountered in real-world scenarios. This enhancement enables the (p, q)-rung linear Diophantine fuzzy sets to be more capable of handling a wide range of complex problems that arise in practical situations, making it a valuable tool for decision-makers looking to tackle real-life issues with precision and reliability. By illustrating the application of this extended method in the context of robot selection problem, the study showcases the practical utility and relevance of the proposed method. Furthermore, a comprehensive evaluation and discussion of the proposed PROMETHEE method is presented, emphasizing its validity, sensitivity, superiority, robustness, and adaptability in addressing real-world decision-making complexities.