Inference error minimisation: fuzzy modelling of ambiguous functions

In this paper, the problem of modelling ambiguous (multi-valued) mappings from noisy experimental data and the use of these models in control strategies are considered. An inference method based on an equation image of a rulebase and minimisation of a performance index (inference error) is described so that the ideal model is the one that minimizes contradiction. Its functional interpretation is used in consistent fuzzy modelling of ambiguous functions. Some function approximation properties are discussed. A feedback linearization control application based on a consistent inversion of a fuzzy model representing a multivalued mapping is finally considered.