Two nonparametric models for fusing heterogeneous fuzzy data

Two models are discussed that integrate heterogeneous fuzzy data of three types: real numbers, real intervals, and real fuzzy sets. The architecture comprises three modules: 1) an encoder that converts the mixed data into a uniform internal representation; 2) a numerical processing core that uses the internal representation to solve a specified task; and 3) a decoder that transforms the internal representation back to an interpretable output format. The core used in this study is fuzzy clustering, but there are many other operations that are facilitated by the models. Two schemes for encoding the data and decoding it after clustering are presented. One method uses possibility and necessity measures for encoding and several variants of a center of gravity defuzzification method for decoding. The second approach uses piecewise linear splines to encode the data and decode the clustering results. Both procedures are illustrated using two small sets of heterogeneous fuzzy data.