Multi-criteria group decision-making using ambiguous sets, Weibull distribution, and aggregation operators: A case study in optimal vendor selection for office supplies

Multi-criteria group decision-making (MCGDM) is a critical process that involves evaluating multiple criteria by a group of decision-makers to arrive at the best possible decision. In this context, this paper advances the framework of ambiguous set (A-AS) and explores the single-valued ambiguous set (SVA-AS) to enhance decision-making accuracy. Furthermore, it introduces novel membership functions based on the Weibull distribution, which offer enhanced capabilities in embracing the inherent ambiguity present within event sets. Expanding on the ambiguous weighted geometric operator (AWMO) introduced by Singh, this study proposes new operator, called ambiguous weighted mean operator (AWMO). This study discusses various definitions and theorems for the AWMO. The advantages of the AWMO lie in its ability to effectively handle decision-making scenarios characterized by ambiguity. By incorporating weights and average geometric operations, AWGO allows for the aggregation of preferences and considerations from multiple decision-makers, resulting in more robust and balanced decision outcomes. By combining SVA-AS, Weibull distribution-based membership functions, AWMO, and entropy, a novel MCGDM method is developed. This method is illustrated through its application in selecting the optimal vendor for office supplies for a medium-sized enterprise. The proposed method demonstrates its effectiveness in MCGDM scenarios through a comparative evaluation against existing approaches.