Error Estimation of Perturbations Under CRI

The analysis of stability and robustness of fuzzy reasoning is an important issue in areas like intelligent systems and fuzzy control. An interesting aspect is to what extent the perturbation of input in a fuzzy reasoning scheme causes the oscillation of the output. In particular, when the error limits (restrictions) of the input values are given, what the error limits of the output values are. In this correspondence, we estimate the upper and lower bounds of the output error affected by the perturbation parameters of the input, and obtain the limits of the output values when the input values range over some interval in many fuzzy reasoning schemes under compositional rule of fuzzy inference (CRI).