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.
DuboisD. and PradeH., Fuzzy sets in approximate reasoning, Part 1: Inference with possibility distributions, Fuzzy Sets and Systems40(1) (1991), 143–202.
2.
HamzaM.F., YapH.J., ChoudhuryI.A., ChiromaH. and KumbasarT., A survey on advancement of hybrid type 2 fuzzy sliding mode control, Neural Computing and Applications (2017), pp. 1–23.
3.
QinJ., A survey of type-2 fuzzy aggregation and application for multiple criteria decision making, Journal of Data, Information and Management1(1) (2019), 17–32.
4.
WuD., Two differences between interval type-2 and type-1 fuzzy logic controllers: Adaptiveness and novelty, Advances in Type-2 Fuzzy Sets and Systems, (2013), pp. 33–48: Springer.
TorshiziA.D., ZarandiM.H.F. and ZakeriH., On type-reduction of type-2 fuzzy sets: A review, Applied Soft Computing27 (2015), 614–627.
7.
KarnikN.N. and MendelJ.M., Centroid of a type-2 fuzzy set, Information Sciences132(1-4) (2001), 195–220.
8.
MendelJ.M. and LiuF., Super-exponential convergence of the Karnik–Mendel algorithms for computing the centroid of an interval type-2 fuzzy set, IEEE Transactions on Fuzzy Systems15(2) (2007), 309–320.
9.
WuD., Approaches for reducing the computational cost of interval type-2 fuzzy logic systems: overview and comparisons, IEEE Transactions on Fuzzy Systems21(1) (2013), 80–99.
10.
ChenY., Study on centroid type-reduction of general type-2 fuzzy logic systems with enhanced opposite direction searching algorithms, Int J Innov Comput Inf Control15(4) (2019), 1425–1439.
11.
Gorzal-czanyM.B., Interval-valued fuzzy controller based on verbal model of object, Fuzzy Sets and Systems28(1) (1988), 45–53.
12.
LiangQ. and MendelJ.M., Equalization of nonlinear time-varying channels using type-2 fuzzy adaptive filters, IEEE Transactions on Fuzzy Systems8(5) (2000), 551–563.
13.
WuH. and MendelJ.M., Uncertainty bounds and their use in the design of interval type-2 fuzzy logic systems, IEEE Transactions on fuzzy systems10(5) (2002), 622–639.
14.
BegianM.B., MelekW.W. and MendelJ.M., Stability analysis of type-2 fuzzy systems, in Fuzzy Systems, 2008. FUZZ-IEEE 2008. (IEEE World Congress on Computational Intelligence). IEEE International Conference on, 2008, pp. 947–953.
15.
LiC., YiJ. and ZhaoD., A novel type-reduction method for interval type-2 fuzzy logic systems, in Fuzzy Systems and Knowledge Discovery, 2008. FSKD’08. Fifth International Conference on, 2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery, 2008, pp. 157–161.
16.
El-NagarA.M. and El-BardiniM., Simplified interval type-2 fuzzy logic system based on new type-reduction, Journal of Intelligent & Fuzzy Systems27(4) (2014), 1999–2010.
17.
ChenY., Study on Centroid Type-Reduction of Interval Type-2 Fuzzy Logic Systems Based on Noniterative Algorithms, Complexity2019 (2019), pp. 7325053, 2019/04/11.
18.
WuD. and MendelJ.M., Enhanced karnik–mendel algorithms, IEEE Transactions on Fuzzy Systems17(4) (2009), 923–934.
19.
MendelJ.M., Uncertain rule-based fuzzy logic systems: introduction and new directions: Prentice Hall PTR Upper Saddle River, 2001.
20.
WuD., A brief Tutorial on Interval type-2 fuzzy sets and systems, Fuzzy Sets and Systems4(1) (2010), 220–225.
21.
MendelJ.M. and LiuX., Simplified interval type-2 fuzzy logic systems, IEEE Transactions on Fuzzy Systems21(6) (2013), 1056–1069.
