Enhanced Interval Type-2 Fuzzy Logic Systems with Improved the Output Processing Using Uncertainty Bounds

It is known that type-2 fuzzy sets let us to model and to minimize the effects of uncertainties in rule-based fuzzy logic system (FLS). While a type-2 FLS has the capability to model more complex relationships, the output of a type-2 fuzzy inference engine needs to be type-reduced. As type-reduction is very computationally intensive, type-2 FLSs may not be suitable for certain real-time applications. This paper aims at developing more computationally efficient output processing consists of type-reduction followed by defuzzification. The type-reduced set is approximated by linear combinations of the inner- and outer-bound sets for the type-reduced set and also the crisp output of type-2 FLS is computed by another. Parameters of these functions are determined during the training phase. By this approach type-2 FLSs can handle such uncertainties in a better way because they provide us with more parameters and more design degrees of freedom. Simulation is presented to demonstrate that the proposed type-reducing and defuzzification algorithms have lower computational cost and better performances than the Karnik-Mendel and Wu-Mendel algorithms.