Interval-Valued Neutrosophic Markov Decision Model for Strategic Planning in the Leisure Sports Industry Competitiveness Analysis under Triple Uncertainty

In contemporary strategic environments, decision-making processes within the leisure sports industry are increasingly challenged by the presence of uncertainty, imprecision, and indeterminacy. Traditional probabilistic frameworks fail to accommodate these complex forms of information granularity. This paper introduces a novel mathematical model by integrating Markov Decision Processes (MDPs) with Interval-Valued Neutrosophic Sets (IVNS) to develop a robust decision-making framework capable of handling triple-layered uncertainty. The proposed model formulates neutrosophic transition probabilities and neutrosophic reward functions, embedding them into a recursive Bellman-like structure that respects neutrosophic arithmetic and logical operations. We rigorously define the model through high-level mathematical formalism, including definitions, properties, and consistency axioms. A numerical case study from the leisure sports industry competitiveness analysis is presented, where alternative strategic actions such as dynamic pricing versus targeted marketing are evaluated under indeterminate consumer behaviors. The example is dissected in a step-by-step manner, highlighting how the neutrosophic framework refines the policy selection process. Results demonstrate the enhanced resilience and flexibility of the model compared to conventional MDPs, confirming its validity in capturing uncertainty at a higher semantic resolution. This paper closes significant theoretical and practical gaps by offering a foundational structure for neutrosophic Markovian models in high-uncertainty industries.