%0 Journal Article
%T A Proposal to Speed up the Computation of the Centroid of an Interval Type-2 Fuzzy Set
%A Carlos E. Celemin
%A Miguel A. Melgarejo
%J Advances in Fuzzy Systems
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/158969
%X This paper presents two new algorithms that speed up the centroid computation of an interval type-2 fuzzy set. The algorithms include precomputation of the main operations and initialization based on the concept of uncertainty bounds. Simulations over different kinds of footprints of uncertainty reveal that the new algorithms achieve computation time reductions with respect to the Enhanced-Karnik algorithm, ranging from 40 to 70%. The results suggest that the initialization used in the new algorithms effectively reduces the number of iterations to compute the extreme points of the interval centroid while precomputation reduces the computational cost of each iteration. 1. Introduction Type-2 fuzzy logic systems (T2-FLS) theory and its applications have grown in recent years [1¨C3]. One of the main problems related to the implementation of these systems is type reduction, which computes the generalized centroid of a type-2 fuzzy set (T2-FS) [4¨C6]. This operation becomes computationally simpler when performed over a particular class of T2-FS, namely, interval type-2 fuzzy set (IT2-FS) [5, 7]. Basically, the centroid of an IT2-FS is an interval [3, 8]. Therefore, computing this centroid can be considered as an optimization problem that finds the extreme points that define the interval [6]. Fast computation of type reduction for IT2-FSs is an attractive problem, which is critical since type-reduction procedures for more general type-2 fuzzy sets (T2-FSs) make use of interval type-2 fuzzy computations [4, 9¨C11]. Up-to-date, several iterative approaches to computing type reduction for IT2-FSs have been proposed [5, 12¨C18]. The Karnik-Mendel (KM) algorithms are the most popular procedures used in interval type-2 fuzzy logic systems (IT2-FLS) [17]. It has been demonstrated that the KM algorithms converge monotonically and superexponentially fast. These properties are highly desirable in iterative algorithms [13]. However, KM procedures converge in several iterations and demand a considerable amount of arithmetic and memory look-up operations [7, 8, 12, 19], for real IT2-FLS implementations. In the case of IT2 fuzzy controllers, the computational cost of type reduction is an important subject [20, 21]. The overall complexity of the controller largely depends on the type-reduction and defuzzification stages. Thus developing strategies for reducing the computational burden and necessary resources for implementing these two stages is highly convenient. In addition, there are other applications of IT2-FLS in which the complexity of the hardware and software platforms
%U http://www.hindawi.com/journals/afs/2013/158969/