Picture Fuzzy Multi-Attribute Decision-Making Approach with Dubois–Prade Aggregation in Industry 6.0

Abstract

Background Multi-Attribute Decision-Making (MADM) involves decision-making problems in which multiple and often conflicting criteria must be considered simultaneously. Such problems frequently involve incomplete data, uncertain information, and subjective judgments from experts. The emergence of Industry 6.0, supported by artificial intelligence (AI), adaptive automation, and advanced analytics, has further increased the complexity of industrial decision-making environments. The continuously evolving nature of industrial technologies and the uncertainty associated with industrial data create challenges in selecting appropriate tools and decision-making methods. Conventional fuzzy models can represent positive and negative judgments; however, their inability to explicitly represent neutral judgments may affect the reliability of decision outcomes. Picture Fuzzy Sets (PFS) provide a more flexible representation by incorporating the degrees of acceptance, neutrality, and rejection. Methods To address the challenges associated with uncertain and interrelated decision information, this study develops two aggregation operators based on the operational laws of Picture Fuzzy Sets and the Dubois–Prade aggregation mechanism. The proposed operators are the Picture Fuzzy Interactive Dubois–Prade Average Aggregation Operator (PFIDPA) and the Picture Fuzzy Interactive Dubois–Prade Ordered Weighted Average Aggregation Operator (PFIDPOWAA). These operators are designed to effectively integrate multi-aspect expert information and provide greater flexibility in handling uncertain and interrelated decision data. The applicability of the proposed framework is demonstrated through a real-world MADM problem involving the selection and adoption of Industry 6.0 using a picture fuzzy decision matrix. Existing aggregation methods are also considered for comparison, and sensitivity analysis is performed to examine the stability of the obtained decision results. Results The proposed PFIDPA and PFIDPOWAA operators effectively aggregate picture fuzzy information while incorporating acceptance, neutrality, and rejection degrees. The application to the Industry 6.0 selection problem demonstrates the ability of the proposed framework to handle uncertain and interrelated decision information. Comparative analysis with existing aggregation methods shows that the proposed Dubois–Prade-based aggregation framework provides flexible and consistent decision outcomes. The sensitivity analysis further indicates that the obtained rankings remain stable under variations in the decision-making parameters. Conclusions The proposed PFIDPA and PFIDPOWAA operators provide an effective framework for MADM problems involving uncertain, incomplete, and interrelated information. By incorporating acceptance, neutrality, and rejection degrees, the proposed picture fuzzy aggregation approach provides a more comprehensive representation of expert judgments. The comparative and sensitivity analyses demonstrate the flexibility, robustness, and reliability of the proposed framework in obtaining stable rankings. Therefore, the proposed aggregation framework can serve as an efficient decision-support tool for Industry 6.0 adoption and other complex decision-making problems involving uncertain information. “‘