Uncertainty bounds and their use in the design of interval type-2 fuzzy logic systems

We derive inner- and outer-bound sets for the type-reduced set of an interval type-2 fuzzy logic system (FLS), based on a new mathematical interpretation of the Karnik-Mendel iterative procedure for computing the type-reduced set. The bound sets can not only provide estimates about the uncertainty contained in the output of an interval type-2 FLS, but can also be used to design an interval type-2 FLS. We demonstrate, by means of a simulation experiment, that the resulting system can operate without type-reduction and can achieve similar performance to one that uses type-reduction. Therefore, our new design method, based on the bound sets, can relieve the computation burden of an interval type-2 FLS during its operation, which makes an interval type-2 FLS useful for real-time applications.