Random generation of fuzzy measures is an important computational task in applied problems related to fuzzy integrals such as the Choquet, Sugeno or Shilkret integrals. In general, a desirable property is the uniformity over the set of fuzzy measures. However, testing this property is not an easy task. In this paper, properties of uniform random fuzzy measures are derived. Special attention is being paid to the families of balanced fuzzy measures, belief measures and possibilities measures. Then, based of such properties, statistical tests for the uniformity of random fuzzy measures are developed. Finally, the uniformity of the most used algorithms is tested using the proposed methods.

Aggregation functions are widely used to fuse information from different sources in a unique value. In many cases, the aggregated information is related to some experimental measure or random sampling of a population. In this direction, it is reasonable to consider aggregation of random elements. In this paper, the concept of aggregation functions of random elements over bounded lattices, which are measurable functions from a probability space to a bounded lattice, is presented. In particular, starting from a partially ordered set, a measurable space is constructed. Random elements are considered to be measurable functions from a probability space to the measurable space. The concept of aggregation of random elements over bounded lattices is defined by generalizing the monotonicity and the boundary conditions in terms of stochastic orders. Several types, such as the induced, random and degenerated aggregations of random elements over bounded lattices are defined and some coherence properties are studied. Particular examples regarding the aggregation of random variables, random graphs and random semi-positive matrices are provided.

In aggregation theory, there exists a large number of aggregation functions that are defined in terms of rearrangments in increasing order of the arguments. Prominent examples are the Ordered Weighted Operator and the Choquet and Sugeno integrals. Following a probability approach, ordering random variables by means of stochastic orders can be also a way to define aggregations of random variables. However, stochastic orders are not total orders, thus pairs of incomparable distributions can appear. This paper is focused on the definition of aggregations of random variables that take into account the stochastic ordination of the components of the input random vectors. Three alternatives are presented, the first one by using expected values and admissible permutations, then a modification for multivariate Gaussian random vectors and a third one that involves a transformation of the initial random vectors in new ones whose components are ordered with respect to the usual stochastic order. A deep theoretical study of the properties of all the proposals is made. A practical example regarding temperature prediction is provided

Aggregation theory is devoted to the fusing of several values into a unique output that summarizes the given information. Typically, the aggregation process is formalized in terms of an increasing mathematical function that maps the input values to the result, fulfilling some boundary conditions. However, this formalization can be too restrictive for some scenarios. In some cases, the inputs can be seen as observations of random variables, the aggregation result being also a random variable. In others, the aggregation process can be identified as a program that performs the aggregation rather than a mathematical function. In this direction, the concepts of aggregation of random variables and computable aggregation have been defined in the literature. This paper is devoted to the definition of computable aggregation of random variables, which are computer programs, not functions, that aggregate random variables, not numbers. Special attention is given to different possible alternatives to modelize random variables and monotonicity. The implementation of some examples is also provided.