Exploration and development of a structured multi-level fusion in an ensemble-based large-scale meta-decision model

Despite significant advancements in Multi-Criteria Decision-Making (MCDM) over recent decades, the absence of formal quality assessments raises concerns about the robustness of these techniques. Ensemble MCDM has emerged as a potential solution to these issues; however, none of the existing studies have addressed how to effectively combine large-scale ranking orders produced by various MCDM techniques or their extended versions, utilizing group decision-makers, multiple fuzzy sets, different aggregation techniques, and parameter tuning. Furthermore, these studies have not developed an ensemble meta-decision model capable of managing a high volume of ranking orders. A multi-level fusion structure can be applied to bridge these gaps. This research aims to explore and develop a structured multi-level fusion within an ensemble-based large-scale meta-decision model. To address this, a new ensemble process structure was developed by integrating a Half-Quadratic Programming (HQP) with MCDM techniques in the meta-decision model, addressing low, intermediate, and high fusion levels. The proposed model was applied to biodiesel selection as an illustrative large-scale example, involving three group decision-makers and incorporating various types of fuzzy sets, aggregation techniques, and parameter tuning indicative of low-level fusion. The matrices resulting from the low-level fusion are then processed individually to generate multiple ranking orders based on decision by opinion score method. This model ensures that the ranking orders, evaluated from different perspectives, represent intermediate-level fusion. This process resulted in 60 distinct ranking orders, which were then used as criteria for another MCDM technique. The large-scale meta-decision model was aggregated using three techniques: the HQP Ensemble, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) with HQP weights, and TOPSIS without weights, reflecting high-level fusion. The results designate that the proposed model effectively mapped the three levels of fusion, showing a high correlation between Experts 2 and 3 but a low correlation with Expert 1. Aggregation techniques per expert correlated well, while different parameters and fuzzy sets had minimal impact on the final rankings. The ensemble model, as a large-scale meta-decision, demonstrated consistency with weighted TOPSIS compared to HQP alone but diverged when ranks were unweighted. Fairness and consensus were key evaluation criteria. The implications of this study suggest that it offers a more objective and robust ranking system compared to individual techniques. Potential research directions could explore compromise ranking to balance consensus with the fair representation of individual methods. Additionally, future trends and emerging advancements in multi-level fusion within MCDM techniques are explored.