A Neutrosophic Monte Carlo Framework for Modeling Indeterminate Participation and Cultural Impact in Tourism Service Quality of Ethnic Sports Events

Ethnic sports tourism involves complex cultural, social, and economic interactions, where uncertainty arises not only from randomness but also from incomplete and contradictory information. Classical probability models cannot fully capture these features. In this paper, we develop a novel Neutrosophic Monte Carlo framework to model participation patterns and cultural impacts in ethnic sports tourism events. Each event is represented by a neutrosophic probability triple (T, I, F), where T measures truth-membership, I measures indeterminacy, and F measures falsity. We introduce a Neutrosophic Expected Value and a Triple-Component Monte Carlo Estimator, and prove strong convergence theorems and variance bounds for the proposed estimators. To enhance efficiency, we design variance reduction techniques adapted to neutrosophic uncertainty, including stratified sampling over cultural and temporal layers and control variates derived from simplified cultural models. A fully computed case study on simulated ethnic sports tourism scenarios demonstrates the accuracy and robustness of our approach, with detailed numerical calculations and tables linking each neutrosophic measure to practical interpretations. The framework establishes a mathematically rigorous and culturally relevant foundation for decision-making in uncertain, heterogeneous tourism systems.