Modeling the uncertainty of a set of graphs using higher-order fuzzy sets

Recent advances in type-2 fuzzy sets (T2FS) have attracted considerable attention for applications in data mining and pattern recognition. In particular, there is an effort in designing granulation procedures able to generate, from raw input measurements, data, granules of information modeled as T2FS. From our viewpoint, the principal aim of those procedures is to embed into the generated T2FS model the key uncertainty characterizing the input data. However, to date there is no formal principle or guideline for the formal evaluation of such granulation procedures in these terms. In this paper, our aim is to define a framework to design and evaluate what we called uncertainty-preserving transformation procedures, which are basically computational procedures that generate, from raw input measurements, information granules modeled as T2FS. In particular, in this chapter, we deal with input measurements that are represented as graphs; hence, a set of graphs G is seen as a set of raw input