Design of Strong Fuzzy Partitions from Cuts

The adoption of triangular fuzzy sets to define Strong Fuzzy Partitions (SFPs) is a common practice in the research community: due to their inherent simplicity, triangular fuzzy sets can be easily derived from data by applying suitable clustering algorithms. However, the choice of triangular fuzzy sets may be limiting for the modeling process. In this paper we focus on SFPs built up starting from cuts (points of separation between cluster projections on data dimensions), showing that a SFP based on cuts can always be defined by trapezoidal fuzzy sets. Different mechanisms to derive SFPs from cuts are presented and compared by employing DC*, an algorithm for extracting fuzzy information granules from classified data