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In this paper the triangular intuitionistic fuzzy numbers are used to express the change factors of the underlying assets of the option in order to describe the uncertainty of the estimated value of the European option price and the hesitation degree of the investors, the intuitionistic fuzzy binomial tree pricing model is made, and the risk neutral pricing method is used to research the single period European call option pricing problem. The findings of the study are that the European option price expressed by a triangular intuitionistic fuzzy number, which can reflect the certainty degree, negation degree and hesitation degree of the investor on the estimated value of the option price, and then the interval value of European option price is obtained by using the cuts sets operation of the triangular intuitionistic fuzzy numbers. Some numerical examples show that European call option price obtained by the triangular intuitionistic fuzzy number can express more the hesitation degree of the investors than the one obtained by the fuzzy number. [ABSTRACT FROM AUTHOR]