Study on weighted-based noniterative algorithms for centroid type-reduction of interval type-2 fuzzy logic systems

Yang Chen; Jinxia Wu; Jie Lan; Yang Chen; Jinxia Wu; Jie Lan

doi:10.3934/math.2020494

AIMS Mathematics

2020, Volume 5, Issue 6: 7719-7745. doi: 10.3934/math.2020494

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Research article

Study on weighted-based noniterative algorithms for centroid type-reduction of interval type-2 fuzzy logic systems

College of Science, Liaoning University of Technology, Jinzhou, Liaoning, 121001, P. R. China

Received: 03 August 2020 Accepted: 07 October 2020 Published: 14 October 2020
MSC : 68XX, 68Uxx

Interval type-2 fuzzy logic systems (IT2 FLSs) have been widely used in many areas. Among which, type-reduction (TR) is an important block for theoretical study. Noniterative algorithms do not involve the complicated iteration process and obtain the system output directly. By discovering the inner relations between discrete and continuous noniterative algorithms, this paper proposes three types of weighted-based noniterative according to the Newton-Cotes quadrature formulas in numerical integration techniques. Moreover, the continuous noniterative algorithms are considered as the benchmarks for computing. Four simulation experiments are provided to illustrate the performances of weighted-based noniterative algorithms for computing the defuzzified values of IT2 FLSs. Compared with the original noniterative algorithms, the proposed weighted-based algorithms can obtain smaller absolute errors and faster convergence speeds under the same sampling rate, which afford the potential values for designing T2 FLSs.
- type-reduction,
- weighted Nagar-Bardini algorithms,
- weighted Nie-Tan algorithms,
- weighted Begian-Melek-Mendel algorithms,
- absolute errors
Citation: Yang Chen, Jinxia Wu, Jie Lan. Study on weighted-based noniterative algorithms for centroid type-reduction of interval type-2 fuzzy logic systems[J]. AIMS Mathematics, 2020, 5(6): 7719-7745. doi: 10.3934/math.2020494

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Abstract

Interval type-2 fuzzy logic systems (IT2 FLSs) have been widely used in many areas. Among which, type-reduction (TR) is an important block for theoretical study. Noniterative algorithms do not involve the complicated iteration process and obtain the system output directly. By discovering the inner relations between discrete and continuous noniterative algorithms, this paper proposes three types of weighted-based noniterative according to the Newton-Cotes quadrature formulas in numerical integration techniques. Moreover, the continuous noniterative algorithms are considered as the benchmarks for computing. Four simulation experiments are provided to illustrate the performances of weighted-based noniterative algorithms for computing the defuzzified values of IT2 FLSs. Compared with the original noniterative algorithms, the proposed weighted-based algorithms can obtain smaller absolute errors and faster convergence speeds under the same sampling rate, which afford the potential values for designing T2 FLSs.

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