Introduction to uncertainty bounds and their use in the design of interval type-2 fuzzy logic systems

In this paper, we derive inner- and outer-bound sets for the type-reduced set of an interval type-2 fuzzy logic system, based on a new mathematical interpretation of the Karnik-Mendel (2001) iterative procedure. The bound sets can not only provide estimates about the uncertainty contained in the output, but can also be used to design an interval type-2 fuzzy logic system. We demonstrate, by means of a simulation experiment, that the resulting system can operate without type reduction and that it can achieve similar performance to one that uses type reduction. Therefore, our new design method, based on the bound sets, can relieve the computational burden of an interval type-2 fuzzy logic system during its operation.