Fuzziness is discussed in the context of fuzzy random variable and a corresponding view of fuzzy martingale and gome their properties are given. Fuzzy random variables are introduced as random variables whose values are not reah but fuzzy sets. In this paper we study fuzzy valued random processes in discrete time and with values in a set of fuzzy sets of separable Banach space.

a b s t r a c tSet valued probability and fuzzy valued probability theory is used for analyzing and modeling highly uncertain probability systems. In this paper the set valued probability and fuzzy valued probability are defined over the measurable space. They are derived from a set and fuzzy valued measure using restricted arithmetics. The range of set valued probability is the set of subsets of the unit interval and the range of fuzzy valued probability is the set of fuzzy sets of the unit interval. The expectation with respect to set valued and fuzzy valued probability is defined and some properties are discussed. Also, the fuzzy model is applied to binomial model for the price of a risky security.

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