Bounded rationality consensus reaching process with regret theory and weighted Moment estimation for multi-attribute group decision making

Probabilistic linguistic term sets perform a particularly active role in the field of decision-making, particularly regarding decision-makers (DMs) who are inclined to convey evaluative information through natural linguistic variables. To effectively improve the current dilemma of multi-attribute group decision-making (MAGDM), this article put forward a new probabilistic linguistic MAGDM method with weighted Moment estimation. First, taking into account the psychological aspect of regret aversion among DMs, we use regret theory to transform the original decision-making matrix into the utility matrix, in which DMs usually exhibit limited rationality during the process of MAGDM. Then, a combined weighting method and a weighted Moment estimation model are investigated to determine the attribute weights, which are more scientifically and reasonably. Subsequently, in the process of consensus reaching process, a new trust propagation mechanism is designed to derive the weights of experts and the adjustment coefficients, in which we consider the shortest and longest propagation paths among DMs. Finally, an empirical validation of the MAGDM method's applicability is conducted utilizing raw coal quality assessment, accompanied by sensitivity and comparative analyses that underscore its advantages and robustness.