Interval type-2 fuzzy logic systems have favorable abilities to cope with uncertainties in many applications. While the block type-reduction under the guidance of inference plays the central role in the systems, Karnik-Mendel (KM) iterative algorithms are standard algorithms to perform the type-reduction; however, the high computational cost of type-reduction process may hinder them from real applications. The comparison between the KM algorithms and other alternative algorithms is still an open problem. This paper introduces the related theory of interval type-2 fuzzy sets and discusses the blocks of fuzzy reasoning, type-reduction, and defuzzification of interval type-2 fuzzy logic systems by combining the Nagar-Bardini (NB) and Nie-Tan (NT) noniterative algorithms for solving the centroids of output interval type-2 fuzzy sets. Moreover, the continuous version of NT (CNT) algorithms is proved to be accurate algorithms for performing the type-reduction. Four computer simulation examples are provided to illustrate and analyze the performances of two kinds of noniterative algorithms. The NB and NT algorithms are superior to the KM algorithms on both calculation accuracy and time, which afford the potential application value for designer and adopters of type-2 fuzzy logic systems.
A closed form type reduction method for piecewise linear interval type-2 fuzzy sets
