In this paper, a fuzzy inventory model with a Weibull deterioration rate, a quadratic demand rate, and a variable holding cost under permissible shortages has been developed. The deterioration rate is expressed by a two-parameter Weibull distribution. During a shortage, some buyers wait for the actual product, while others do not. This shortfall is considered partially backlogged in this model. Some buyers wait for the actual product during such shortages, but many do not. Therefore, partially backlogged shortages are taken into account in this approach. In a traditional inventory model, all parameters such as purchasing cost, shortage cost, holding cost, etc. are predetermined. However, there will be some variations. As a result, fuzzy factors are more accurate to deal with the real world’s problems. This research attempts to cut down the cost in a fuzzy environment by using quadratic demand, shortage, Weibull deterioration rate, and variable holding cost. Costs such as ordering, shortage, and deterioration are addressed as pentagonal fuzzy numbers that are defuzzified using a graded mean representation approach. Finally, sensitivity analysis was carried out to investigate the influence of cost parameters on total inventory cost. A numerical example is used to validate the proposed model in a real-world system.