This paper introduces the concept of fuzzy random variables, which are random variables whose values are not real numbers but fuzzy numbers. Fuzziness is discussed in the context of multivalued logic, where statements can have truth values in the interval [0, 1], and fuzzy sets are defined as indexed sets of such statements. Fuzzy random variables are then defined as mappings from a probability space to the set of fuzzy numbers, with the membership function of each fuzzy number representing the probability of a specific value being observed. The paper defines several key concepts, including the expectation of a fuzzy random variable, probabilities associated with fuzzy random variables, and conditional expectations and probabilities. Theorems are provided to establish properties of these concepts, such as the expectation of the product of two fuzzy random variables and the joint probability of two fuzzy random variables. The paper also discusses independent fuzzy random variables and their properties, such as the equality of the expectation of the product of two independent nonnegative fuzzy random variables.This paper introduces the concept of fuzzy random variables, which are random variables whose values are not real numbers but fuzzy numbers. Fuzziness is discussed in the context of multivalued logic, where statements can have truth values in the interval [0, 1], and fuzzy sets are defined as indexed sets of such statements. Fuzzy random variables are then defined as mappings from a probability space to the set of fuzzy numbers, with the membership function of each fuzzy number representing the probability of a specific value being observed. The paper defines several key concepts, including the expectation of a fuzzy random variable, probabilities associated with fuzzy random variables, and conditional expectations and probabilities. Theorems are provided to establish properties of these concepts, such as the expectation of the product of two fuzzy random variables and the joint probability of two fuzzy random variables. The paper also discusses independent fuzzy random variables and their properties, such as the equality of the expectation of the product of two independent nonnegative fuzzy random variables.