Fusing heterogeneous fuzzy data for clustering

One goal of sensor-fusion methods is the integration of data of various types into a common usable form. Here we seek a uniform framework for the following three types of data: (1) numerical (e.g., x = 74.1); (2) interval (e.g., x = [73.9,75.2]); and (3) fuzzy (e.g., x = tall, where tall is described by a suitable membership function). The problem context of this paper is clustering, which is the problem of separating a set of objects into self-similar groups, but other types of data analysis can be handled similarly. Earlier work on this problem has produced both parametric and nonparametric approaches. The parametric approach is only possible in cases when all the fuzzy data have membership functions coming from a single parametric family of curves, and in that case, the specific parameter values provide numerical data that can easily be used with standard clustering techniques such as the fuzzy c-means algorithm. The more difficult and interesting problem involves the nonparametric case, where there is not a common parametric form for the membership functions. The earlier nonparametric approach produces numerical data for clustering via necessity and possibility values which are derived using a set of `cognitive landmarks'. The main contribution of this note is in presenting a new, simpler nonparametric approach that derives a common usable form of data directly from the membership functions. The new approach is described and then demonstrated using a specific example.