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The relationship between physical exercise and mental health in university students is characterized by complexity, ambiguity, and contextual variability. Traditional modeling approaches often fail to capture the indeterminate, uncertain, and contradictory nature of these interactions. In this study, we introduce a novel analytical framework based on Neutrosophic Cognitive Maps (NCMs) to model and examine the multidimensional effects of exercise interventions on the mental health of university students. NCMs extend Fuzzy Cognitive Maps by integrating the concept of indeterminacy, allowing experts to express not only positive or negative causal relationships but also undefined or inconclusive ones. This approach is particularly suitable for modeling psychosocial systems, where subjective interpretation and ambiguity are common.We construct an NCM with ten interrelated concepts ranging from exercise intensity, sleep quality, and academic stress to anxiety levels and social support and encode the causal influences among them using neutrosophic logic. Through iterative simulations and matrix-based transformations, we analyze the dynamic behavior of the system, identify equilibrium states (fixed points), and explore the emergence of limit cycles. The results reveal nuanced interaction patterns that highlight the moderating and mediating roles of indeterminate factors, such as emotional volatility and environmental context, in shaping mental health outcomes. This paper provides a mathematically rigorous yet intuitively interpretable tool for researchers and practitioners in health sciences and psychology. It opens new pathways for the design of adaptive, personalized mental health interventions grounded in systems thinking and neutrosophic logic.

Abstract licence: CC BY-NC

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