In today’s highly competitive business environment, inventory management plays a very important role in supply chain management to ensuring smooth operation and maximizing profitability. This paper aims to create a simple leakage inventory model in a fuzzy environment with either instantaneous or finite production rates that avoids shortages. In any inventory system, goods in stock may possess the properties of deterioration, perishability, or leakage. A decline in quality with a relatively constant quantity is referred to as deterioration. On the other hand, leakage indicates the decrease in quantity over a predetermined period of time while retaining constant quality. The objective here is to determine the Optimal Economic order lot size (EOQ) to maximize the annual total profit. Since carbon emissions have an impact of carbon emissions on accelerating global warming, it is imperative to focus on reducing carbon emissions. The fuzzy numbers and fuzzy values are widely used in many applications for representing uncertain information. This paper integrates the cost of carbon emissions into the total inventory cost. Certain uncertain inventory parameters are represented by fuzzy numbers, and the optimal solution is obtained through the signed distance method. To validate the model, a numerical example is provided.