A method for considering and processing measurement uncertainty in Fuzzy Inference Systems

Fuzzy inference systems are generally employed to deal with complex systems, when a high model uncertainty is present in processing signals and data related to those systems. In most presently available fuzzy inference systems, uncertainty is not assigned to input data, even when they come from an experimental, in-field process. Recent proposals showed that fuzzy and random-fuzzy variables can be usefully employed to represent and process uncertainty in measurement, in close agreement with the metrology concepts defined in the presently available standards. Taking into account that the mathematical foundations of the fuzzy inference systems and the random-fuzzy variables are the same, this paper proposes an original, generalized approach to fuzzy inference systems, where the input quantities are random-fuzzy variables, so that measurement uncertainty can be considered throughout the whole fuzzy inference. The proposed method is applied to the classical example of the inverted pendulum control.