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Given that the majority of existing approaches for multi-criteria group decision making (MCGDM) rely solely on the preferences of decision makers (DMs) and fail to consider the various relationships between alternatives, this paper attempts to model the relevant relational structures using graphs and introduce the concept of graph neural networks (GNNs) in the context of group decision-making. By leveraging the powerful expressive capabilities of GNNs, the aim is to mine additional information pertinent to the decision-making process and screen out alternatives for the final decision. To begin, we provide a mapping of MCGDM to the graph domain and construct a corresponding relation graph among alternatives. Additionally, to deal with uncertain or vague information, we transform the group decision-making problem into a Pythagorean fuzzy environment and define a novel measure of entropy specifically designed for Pythagorean fuzzy sets (PFSs) in the entropy weight model to determine the weights of criteria. Simultaneously, we propose a new distance measure for PFSs, which is then applied to the extended Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method to rank alternatives. Furthermore, we develop a GNNs-based Pythagorean fuzzy MCGDM approach that incorporates the aforementioned techniques for group decision-making. Finally, to validate the effectiveness and superiority of this approach, we employ it to address a supplier selection issue. Compared with baseline group decision-making approaches, our approach can indeed capture the relationships among alternatives in complex group decision-making scenarios and outperforms the best-performing baseline by nearly 2.8% in terms of ranking accuracy. • A mapping from multi-criteria group decision making to the graph domain is provided. • A normalized entropy measure is defined in Pythagorean fuzzy sets. • A modified Pythagorean fuzzy distance measure is proposed. • A Pythagorean fuzzy group decision-making approach based on graph neural networks is developed. [ABSTRACT FROM AUTHOR]

In this paper, we propose a Generalised-Fuzzy-TOPSIS method as a versatile evaluation model. The model is suitable for different types of fuzzy or interval-valued numbers, with or without subjective weights of criteria being defined by evaluators. Additionally, we extend the final ranking step of the TOPSIS method, which is the calculation of closeness coefficient based on the separation from Negative Ideal Solution (NIS) and proximity to Positive Ideal Solution (PIS). Experiments show that with the same focus on PIS and NIS distances, our proposed ranking is identical to TOPSIS, and also performs very well when varying the distance weights. The applicability of the proposed method is demonstrated with relevant examples of technology and material selection in the context of additive manufacturing. Sensitivity analyses, based on subjective weights of criteria, degree of optimism, evaluators’ weights in group decision making, and distance weights, are presented to assist managers in making more informed decisions. [ABSTRACT FROM AUTHOR]