Complex linear Diophantine fuzzy Dombi prioritized operators-based MULTIMOORA approach with applications to sustainable energy planning

Sustainable energy planning is a critical challenge, particularly in regions with complex decision-making environments and uncertain data. The selection of an optimal energy source requires robust methodologies that can effectively handle multi-criteria decision-making (MCDM) under uncertainty. This study explores the application of the multiple objective optimization on the basis of ratio analysis plus full multiplicative form (MULTIMOORA) method by incorporating the concept of the complex linear Diophantine fuzzy ([Formula: see text]) set. The [Formula: see text] set extends the conventional linear Diophantine fuzzy set by introducing a phase component, thereby enhancing the system's adaptability. To examine the interrelationships among multiple [Formula: see text] numbers, we develop the [Formula: see text] Dombi prioritized averaging ([Formula: see text]) and the [Formula: see text] Dombi prioritized geometric ([Formula: see text]) aggregation operators, along with their weighted versions, based on the proposed Dombi operational laws. The fundamental properties of these aggregation operators are systematically analyzed. The developed [Formula: see text] operators are then integrated into the MULTIMOORA method to address MCDM problems. To illustrate the practical effectiveness of the proposed framework, a case study is conducted to determine a sustainable energy source for Gwadar, Pakistan, utilizing [Formula: see text] information. Furthermore, comparative analyses are performed against existing methodologies to validate the applicability and accuracy of the proposed approach.