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

Abstract

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.

DOI: 10.5281/zenodo.16887773