<p>This paper proposes a novel model for addressing the multiple attribute group decision-making (MAGDM) problems in the picture fuzzy sets (PFSs) and presents a methodology for measuring the reliability of the proposed MAGDM model in the meanwhile. The new model consists of three main parts: first, in order to integrate the information of decision-makers (DMs) and consider the existence of priority relationships among DMs, the prioritized aggregation operator (AO), and operation laws based on Sugeno–Weber norms are introduced into PFSs to construct picture fuzzy prioritized Sugeno–Weber average (PFPSWA) operator, picture fuzzy prioritized Sugeno–Weber geometric (PFPSWG) operator and their weighted forms (PFPSWWA, PFPSWWG), and related properties of AOs are also explored. Secondly, the weights of the attributes are determined by an extended maximizing deviation method. Among these, a novel distance measure is proposed to address the limitations of existing distance measures. Additionally, related properties of this distance measure are discussed. Thirdly, the ranking of alternatives is accomplished by the Elimination Et Choice Traduisant la Réalité (ELECTRE) III approach. Then, a measure is proposed for calculating the reliability of the PFSs information. Accordingly, the MAGDM model is analyzed based on fault tree analysis with the aim of determining the reliability of the decision-making method. Finally, the paper demonstrates the efficiency of the proposed method by using a shopping mall siting example.</p>