On the Transformation of Fuzzy Measures to the Power Set and Its Role in Determining the Measure of a Measure

We are interested in developing a framework for determining the degree of satisfaction of some imprecisely stated conditions by some relevant variables whose value itself may be imprecise or uncertain. We particularly focus on the use of fuzzy measures as they can provide a unified representation of various types of uncertainty and imprecision. Starting with set measures, mappings from crisp sets into the unit interval, we first discuss the extension of these to provide measures of fuzzy subsets. We next consider the issue of allowing measures to assign values to other measures. This requires the transformation of the set measure to be a measure on the power set. We then look at some methods for transforming measures to the power set.