On The Issue of Learning Weights from Observations for Fuzzy Signatures

We investigate the issue of obtaining weights, which are associated with aggregation in fuzzy signatures, from real world data. Our approach will provide a way to extract the relevance of lower levels to the higher levels of the hierarchical fuzzy signature structure. We also handle the non-differentiability of max-min aggregation functions for gradient based learning. A mathematically proved method, which is found in the literature to approximate the derivatives of max-min functions, has been used.