An overview of alternative type-reduction approaches for reducing the computational cost of interval type-2 fuzzy logic controllers

Interval type-2 fuzzy logic controllers have demonstrated better abilities to handle uncertainties than their type-1 counterparts in many applications; however, the high computational cost of the iterative Karnik-Mendel algorithms in type-reduction may hinder them from certain real-time applications. This paper provides an overview and comparison of 11 alternative type-reducers, which have closed-form representations and are more convenient in analysis. Experiments demonstrate that 10 of them are faster than the Karnik-Mendel algorithms. Among them, the Wu-Tan and Nie-Tan methods are the fastest, and they are only about 1.2-1.7 times slower than a type-1 fuzzy logic controller.