Optimal Speed Controller Design with Interval Type-2 Fuzzy Sets

Abstract

Interval type-2 fuzzy sets are often used in the designing of fuzzy systems associated with the speed control under uncertainty. In this paper, we consider the possibilities of using interval type-2 fuzzy sets to describing the uncertainties that arise when defining input variables. These uncertainties can be presented as the different meanings on the same dynamic system or changes in the technical parameters that occur due to external factors. We also present complex interval type-2 fuzzy sets and give the examples of their use to reduce the number of fuzzy sets and rules in a fuzzy knowledge base. The necessary conditions for the construction of complex interval type-2 fuzzy sets and methods for determining lower and upper membership functions in them are also given. The footprint of uncertainty for the complex interval type-2 fuzzy set is presented with upper and lower membership functions of different fuzzy sets. All methods which are described in this work can be used in decision support systems design, to select the optimal parameters of a nonlinear system, or in fuzzy speed controller design.