Abstract
Interval type-2 fuzzy logic systems (IT2FLSs) have better abilities to cope with uncertainties in many applications. One major drawback of IT2FLSs is the high computational cost of the iterative Karnik-Mendel (KM) algorithms in type-reduction (TR). From the practical point of view, this prevents using IT2FLS in real-world applications. To address this issue, a novel non-iterative method called Moradi-Zirkohi-Lin (MZL) TR method is proposed for computing the centroid of an IT2FLS. This makes the practical implementation of the IT2FLSs simpler. Comparative simulation results show that the proposed method outperforms the KM TR method in terms of computational burden. Besides, closer results, in terms of accuracy, to the KM TR method among the existing non-iterative TR methods are also achieved by the proposed TR method.
Highlights
In 1975, Type-2 fuzzy sets (T2FSs) were introduced by Zadeh for the first time [1]
A novel non-iterative method called Moradi-Zirkohi (MZ) type reduction (TR) method is proposed for computing the centroid of an interval type-2 fuzzy logic systems (IT2FLSs)
To make the practical implementation of the IT2FLSs simpler, much research has been devoted to providing non-iterative approaches for computing the centroid of an IT2FLS
Summary
In 1975, Type-2 fuzzy sets (T2FSs) were introduced by Zadeh for the first time [1]. The membership functions (MFs) in a T2FS are themselves a type-1 fuzzy set (T1FS) instead of crisp numbers in a T1FS. The KM TR method is an iterative method which needs several iterations to converge This problem does not have any closed form solutions. In [9], it has been shown that the enhanced opposite direction searching (EODS) algorithms are among the most rapid algorithms for practical IT2FLSs. The EODS has been extended for computing the centroid TR of general type-2 fuzzy logic systems [10]. To make the practical implementation of the IT2FLSs simpler, much research has been devoted to providing non-iterative approaches for computing the centroid of an IT2FLS. The uncertainty bound (UB) method can be considered as a famous non-iterative method [13]. Another closed-form TR and defuzzification method, known as the Begian-Melek-Mendel (BMM) algorithms, was proposed in [14]. In [17], a comparison is made between some non-iterative algorithms
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