The author extends the notion of obtaining probabilities from observations of a random experiment to incorporate fuzzy subset theory. A probability measure P_F(E) is derived for fuzzy event E being equal to :9I where n = a fuzzy subset measuring the degree to which B_i representing outcomes of a random variable V, and :9I = a fuzzy subset measuring the degree to which B_i is contained in E.

This is shown to be a true generalization of traditional (non-fuzzy) probability measures. This includes showing _f(x) = 1 for x = the set of all values for V, :9I When E is crisp (non-fuzzy), then the traditional probability measure occurs.

The author uses a definition of specificity to measure the amount of information in the observations. The measure is the integral over the variable :G a of the inverse of the cardinality of the :G a -level set (the crisp set of values whose membership function equals or exceeds :G a). The informativeness of a fuzzy set is the log of the product of this specificity measure times the cardinality of the set. Moreover, conditional probabilities are defined and discussed in this context, as are means. As the author points out, this could be the beginning of a theory of fuzzy statistics.