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  • https://doi.org/10.1007/s40815-025-02190-yCopy DOI Icon

Refined Neutrosophic Cognitive Maps: A Novel Framework for Modeling Indeterminate Causal Relationships

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Abstract

Abstract Fuzzy cognitive maps (FCMs) are widely used for modeling complex systems and supporting explainable AI. However, traditional FCMs cannot effectively represent indeterminacy that arises from incomplete or conflicting information. Neutrosophic cognitive maps (NCMs) extended FCMs to handle such uncertainty, but their use of a single indeterminate symbol (I) limits their ability to model complex, real-world interactions. This paper introduces Refined neutrosophic cognitive maps (RNCMs), a novel framework that combines single-valued neutrosophic sets (SVNSs) for representing concept states with a new refined dual neutrosophic set (RDNS) for modeling causal relationships. RNCMs capture five distinct causal relationships—positive to positive, positive to negative, negative to positive, negative to negative, and indeterminate to indeterminate—allowing a richer and more precise modeling of dual and uncertain relationships than FCMs or NCMs. A case study on students’ academic performance demonstrates that RNCMs reproduce the outputs of FCMs and NCMs while uncovering additional causal nuances, such as polarity shifts and the distinction between genuine indeterminacy and measurable influence. RNCMs also reveal when positive states in certain factors lead to negative outcomes—insights that earlier models fail to capture. Although the model requires higher computational effort, it remains robust across thresholds and provides better explainability and interpretability. Overall, RNCMs advance cognitive map modeling by integrating refined uncertainty handling with dual causal relationships, making them a powerful and explainable tool for complex decision-making systems.

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