Plithogenic cognitive maps with extended plithogenic representations & applications

This chapter introduces Extended Plithogenic Cognitive Maps (EPCM), a novel decision-making framework that integrates extended plithogenic set representations with plithogenic cognitive maps (PCM) to model complex decision environments characterized by conflicting, uncertain, and multi-dimensional relationships. Unlike conventional plithogenic cognitive maps, which primarily consider superior attribute values, the proposed EPCM framework simultaneously incorporates superior and inferior attribute values, thereby enabling a more comprehensive representation of acceptance and denial dynamics in managerial reasoning. The methodological foundation of EPCM is formally established through extended plithogenic representations defined by discrepancy degrees relative to both positive and negative attribute extremities, coupled with plithogenic aggregation operators and iterative fixed-point cognitive inference. To demonstrate the effectiveness of the proposed approach, the framework is applied to a managerial decision-making problem involving the promotion of IoT-based manufacturing systems, where inter-associational impacts among strategic factors such as automation, supply-chain digitalization, business analytics, technological infrastructure, and data security are evaluated under the attributes of quality, cost, and reliability. Comparative analysis reveals that EPCM provides greater specificity and interpretability than conventional plithogenic cognitive maps by explicitly accounting for attribute-value sensitivity and contextual managerial priorities. The proposed framework establishes a new generation of plithogenic cognitive decision models capable of addressing industrial complexity, strategic planning, sustainability challenges, and uncertainty-aware managerial optimization, opening avenues for broader applications in business analytics and intelligent decision support systems.