Choquet fuzzy integral based verification of handwritten signatures

Abstract

For dealing with adjacent input fuzzy sets having overlapping information, non-additive fuzzy rules are formulated by defining their consequent as a function of fuzzy measures, i.e., a simple form of Choquet integral. The fuzzy measures aggregate the information from the overlapping fuzzy sets using the λ-measure. The defuzzified output of these rules is also in the general form of the Choquet fuzzy integral. The underlying non-additive fuzzy model is investigated for both identification and control of non-linear systems. The identification of this fuzzy model involves the strength of the rules as the known input functions and fuzzy densities required to compute fuzzy measures as the unknown functions to be estimated. The use of q-measure provides a more flexible and powerful way of simplifying the computation of λ-measure used to take account of interaction between the fuzzy sets. This model has been successfully applied to the real life problem of verifying the authenticity of offline signatures.