A novel ORESTE approach for MAGDM incorporating probabilistic interval-valued linguistic information: case studies in higher education quality and the energy industry

Multi-attribute group decision making (MAGDM) is a pivotal tool in diverse evaluations. However, existing approaches often overlook attribute ambiguity and interrelationships, leading to unreliable outcomes. This article introduces a novel MAGDM support scheme that extends the widely accepted ORESTE (organísation, rangement et Synthese dèdonnees relarionnelles, in French) method to the context of Probabilistic Hesitant Interval-Value Sets (PHIVSs). PHIVSs integrate Hesitant Fuzzy Linguistic Terms (HFLTs) and Probabilistic Linguistic Term Sets (PLTSs) and transform conventional linguistic terms into interval-based expressions. This augmentation significantly extends their applicability in MAGDM scenarios, particularly those marked by elevated uncertainty. The conventional ORESTE model, a standard MAGDM tool, encounters limitations in intricate scenarios, resulting in data loss and necessitating more adaptive solutions. Our integrated PHIVS approach overcomes these challenges by incorporating fuzzy representation into ORESTE, enabling robust MAGDM solutions. Preferences are classified into three intensities based on likelihoods, establishing a structured Preference Intensity Relation (PIR). PIR effectively discerns among alternatives, elucidating preferences, indifference, or incomparability. This distinction proves invaluable in complex and uncertain decision-making across diverse domains. A key innovation of our approach lies in the unexplored application of PHIVS and ORESTE in MAGDM. Utilizing probability measures for PHIVSs, we establishes precise binary connections among alternatives for enhancing assessment and prioritization. The representation of evaluations with PHIVS and integration of likelihood measures offer an efficient solution for intricate MAGDM problems, particularly those laden with uncertainty. To illustrate the utility of our approach, we provide two comprehensive examples. These examples showcase the practicality and effectiveness of our approach in real-world assessments, highlighting its significance in advancing decision-making methodologies.