Choquet fuzzy integral based modeling of non-linear system

Abstract

For dealing with the adjacent input fuzzy sets having overlapping information, non-additive fuzzy rules are formulated by defining their consequent as the product of weighted input and a fuzzy measure. With the weighted input, need arises for the corresponding fuzzy measure. This is a new concept that facilitates the evolution of new fuzzy modeling. The fuzzy measures aggregate the information from the weighted inputs using the λ-measure. The output of these rules is in the form of the Choquet fuzzy integral. The underlying non-additive fuzzy model is investigated for identification of non-linear systems. The weighted input which is the additive S-norm of the inputs and their membership functions provides the strength of the rules and fuzzy densities required to compute fuzzy measures subject to q-measure are the unknown functions to be estimated. The use of q-measure is a powerful way of simplifying the computation of @l-measure that takes account of the interaction between the weighted inputs. Two applications; one real life application on signature verification and forgery detection, and another benchmark problem of a chemical plant illustrate the utility of the proposed approach. The results are compared with those existing in the literature.