<p>Environmental concerns arising from industrial carbon emissions—generated during production, transportation, storage, and fuel consumption—have significantly influenced modern inventory and supply chain decisions. This study develops a fuzzy inventory model incorporating carbon taxation policies to mitigate emissions during production. Demand, a critical factor affecting industrial revenue, is considered stochastic and modeled as a fuzzy variable to capture real-world uncertainty. The model integrates machine-based inspection processes, which enhance efficiency and reduce inspection time compared to traditional human-based methods, thereby lowering inventory costs. A learning effect is incorporated to represent reductions in repetitive production efforts over time. The purchaser categorizes received items into good, defective, and waste, with labor and inspection costs influencing overall profitability. To address uncertainty in defective items, the expected defective proportion is estimated using Chi-square and Beta distributions. The inclusion of both distributions allows the proposed model to capture different probabilistic characteristics of defective items. Additionally, advertising and salvage strategies are incorporated to improve sales performance, particularly under uncertain demand conditions. The objective is to maximize the buyer’s fuzzy profit by optimizing lot size and selling price under both distributional assumptions, while considering carbon taxation and learning effects. A comparative analysis reveals that the fuzzy profit behavior aligns more closely with the Chi-square distribution than the Beta distribution. A numerical example is provided to validate the proposed model and demonstrate the impact of key parameters on the buyer’s total fuzzy profit.</p>