Multistage fuzzy inference formulated as linguistic-truth-value propagation and its learning algorithm based on back-propagating error information

Multistage fuzzy inference, where in the consequence in an inference stage is passed to the next stage as a fact, is studied and formulated as a type of linguistic-truth-value propagation, based on a concept of linguistic similarities between conditional propositions in successive stages. The formulation is useful in studying the characteristics of multistage fuzzy inference and reveals its structural relationship to multilayer perceptrons. The learning algorithm for multistage fuzzy inference is then derived, using backpropagating error information. The algorithm provides a means of automatically training the multistage fuzzy inference network, using input-output exemplar patterns. Intermediate membership functions based on simulation results, which are generated automatically in the intermediate stage, are proposed. The intermediate stage fuzzy-classifies the input space using intermediate membership functions. In this way, intermediate membership functions provide information regarding regional characteristics in exemplar patterns