The article explores different pricing formulas for American basket options in uncertain financial environments. It focuses on four types of options: American arithmetic basket call, American arithmetic basket put, American geometric basket call, and American geometric basket put options. The researchers derived pricing formulas based on uncertain differential equations for stock prices and provided numerical examples to demonstrate their effectiveness. The study shows that basket options are generally cheaper than portfolios of individual assets, making them popular among investors. The relationship between option price and various parameters is also discussed.