An obviously important aspect of target tracking, and more generally, data fusion, is the combination of those pieces of multi-source information deemed to belong together. Recently, it has been pointed out that a random set approach to target tracking and data fusion may be more appropriate rather than the standard point-vector estimate approach -- especially in the case of large inherent parameter errors. In addition, since many data fusion problems involve non-numerical linguistic descriptions, in the same spirit it is also desirable to be able to have a method which averages in some qualitative sense random sets which are non-numerically- valued, i.e., which take on propositions or events, such as 'the target appears in area A or C, given the weather conditions of yesterday and source 1' and 'the target appears in area A or B, given the weather conditions of today and source 2.' This leads to the fundamental problem of how best to define the expectation of a random set. To date, this open issue has only been considered for numerically-based random sets. This paper addresses this issue in part by proposing an approach which is actually algebraically-based, but also applicable to numerical-based random sets, and directly related to both the Frechet and the Aumann-Artstein-Vitale random set averaging procedures. The technique employs the concept of 'constant probability events,' which has also played a key role in the recent development of 'relational event algebra,' a new mathematical tool for representing various models in the form of various functions of probabilities.