Picture fuzzy Aczel–Alsina power geometric aggregation operators with confidence level and their application to multi-criteria decision-making

This study proposes a picture fuzzy decision-making framework that incorporates power aggregation operators grounded in Aczel–Alsina operations. These operators are adept at capturing the relationships among multiple criteria, thereby improving the precision of decision-making outcomes. The framework also integrates the confidence levels of decision makers based on their familiarity with the evaluated alternatives into the picture fuzzy setting alongside core data. Building on the operational foundations of Aczel–Alsina functions, the research introduces novel confidence-based picture fuzzy Aczel–Alsina power-weighted and ordered-weighted geometric operators, allowing the inclusion of expert knowledge in the aggregation process. Additionally, the mathematical properties and structural features of these new operators are examined in detail. To validate their practical utility, the operators are applied to a multi-criteria decision-making problem in the food industry. Comparative analysis with existing methods demonstrates the enhanced effectiveness of the proposed approach in managing uncertainty and addressing complex decision-making challenges.