There is no accurate answer for the question, which method of modeling of uncertainty is preferable: random or fuzzy. Today both of these approaches are highly popular. Fuzzy and probabilistic approaches are commonly used for modeling of uncertainty.

Fuzzy numbers can be used for modeling vagueness of parameters, such as risk-free rate or volatility in option pricing. Under these assumptions, option value depends on believe degree and turns to fuzzy number. In this paper the Black – Scholes formula and it’s modification for American option arbitrage-free value are used. Fuzzy representations of underlying asset price, volatility of asset price and risk-free rate are used as parameters. There is set of papers regard ing fuzzy approach for European option pricing. In this paper fuzzy approach is used for arbitrage-free American option pricing for the first time. The fuzzy American call value is compared with fuzzy European option value.