Q-scale measures of fuzzy sets

In an attempt to generalize Nahmias' scale measure to apply to fuzzy sets, in this paper we introduce the notion of Q-scale measure. A Q-scale measure is slightly different from a crisp-valued possibility measure in several ways. We use a number of examples to demonstrate the validity of the notion of Q-scale measure in various circumstances and give preliminary discussions on basic properties of Q-scale measure, induced Q-scale measure, semigroup of Q-scale measures, Q-scale measure of probabilistic sets, and Q-scale measure of L-fuzzy sets.