Instrumental Uncertainty and Model Uncertainty Unified in a Modified Fuzzy Inference System

When complex systems are considered, a deterministic approach is often too complex or impossible to be implemented. In such a case, fuzzy inference systems (FISs) can be employed to consider model uncertainty. However, in most currently available FISs, instrumental uncertainty is not considered, so that the input data, even when they come from an experimental in-field process, are crisp values. The few available approaches that try to take into account uncertainty on the input data assign a different meaning to the uncertainty concept, as compared with that considered in metrology. Recent proposals have represented and processed measurement results, together with their associated uncertainty, in terms of fuzzy and random-fuzzy variables (RFVs), in full compliance with the metrology concepts defined in the currently available standards. Since the FISs and the RFVs have the same mathematical foundations, this paper considers and applies an original generalized approach to FISs to the classical example of the inverted pendulum control. In this generalized approach, the input quantities are RFVs, and measurement uncertainty is considered throughout the whole fuzzy inference.