<p>Evolutionary game theory constitutes a fundamental mathematical framework for forecasting behavior in infinite population systems with perfect rationality. However, practical applications face challenges related to strategic decision-making under finite population constraints and pervasive uncertainty in payoff elicitation and preference articulation. Existing analytic models are insufficient for addressing epistemic constraints (individual cognition) and aleatoric variability (environmental indeterminacy) in these games. To bridge this gap, we propose a probabilistic linguistic stochastic evolutionary game framework, which utilizes probabilistic linguistic term sets to formalize qualitative payoff uncertainty. Additionally, we develop probabilistic fuzzy Moran processes with heterogeneous interaction operators. The dynamics of strategy fixation under stochastic environments are then analyzed. Finally, we apply the proposed methods to enterprise carbon neutrality decision-making. Case study results demonstrate substantial validity and operational effectiveness, indicating that our probabilistic linguistic stochastic evolutionary game provides a systematic approach to behavioral analysis in finite populations with informational uncertainty and interaction heterogeneity.</p>