Kernel density estimation is a popular non-parametric method for estimating the probability density function of a random variable. However, classical kernel density estimation assumes all observations are exact, limiting its applicability in scenarios involving uncertainty or indeterminacy. To overcome this limitation, we introduce a generalized interval-valued method based kernel density estimation framework based on generalized interval-valued method. This method integrates indeterminacy into the estimation process, enhancing flexibility and robustness. Using Gaussian and Epanechnikov kernels, we extend classical bandwidth selection theory to incorporate generalized interval-valued method parameters. Comprehensive studies, including train and test models, highlight its applications in artificial intelligence and environmental data analysis. The results demonstrate that generalized interval-valued method based kernel density estimation effectively handles uncertainty, improving accuracy in estimating probability density functions under imprecise data conditions. This advancement significantly broadens the utility of kernel density estimation, making it highly suitable for complex and uncertain datasets in various domains.