On generalized measures of realization in uncertain environments

We concern ourselves with the problem of determining the overall degree or measure of realization of an object based upon its occurrence in a collection of individual phenomena. We show that while probability is the classic measure of this type, it is but one of a whole family of possible such measures. We use the OWA operator to provide this family of measures. We investigate the situation in which our observations are both specific elements and subsets of some base set.