Design of reasonable initialization weighted enhanced Karnik-Mendel algorithms for centroid type-reduction of interval type-2 fuzzy logic systems

Yang Chen; Jiaxiu Yang; Chenxi Li; Yang Chen; Jiaxiu Yang; Chenxi Li

doi:10.3934/math.2022549

AIMS Mathematics

2022, Volume 7, Issue 6: 9846-9870. doi: 10.3934/math.2022549

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Research article

Design of reasonable initialization weighted enhanced Karnik-Mendel algorithms for centroid type-reduction of interval type-2 fuzzy logic systems

College of Science, Liaoning University of Technology, Jinzhou, Liaoning, 121001, China

Received: 22 December 2021 Revised: 01 March 2022 Accepted: 04 March 2022 Published: 18 March 2022
MSC : 68XX, 68Uxx

Interval type-2 fuzzy logic systems (IT2 FLSs) already become an emerging technology in recent years. As the most popular type-reduction (TR) algorithms, Karnik-Mendel (KM) algorithms own the advantage of maintaining the uncertainties flow in systems. This paper analyzes the initialization for KM types of algorithms. Furthermore, the weighting approaches of them are also given by means of the Newton-Cotes quadrature formulas. Importantly, the reasonable initialization weighted enhanced Karnik-Mendel (RIWEKM) algorithms are provided to complete the centroid type-reduction of IT2 FLSs. Three computer simulation experiments illustrate that, the proposed RIWEKM algorithms own both smaller absolute errors and faster convergence speeds in contrast to the EKM and RIEKM algorithms.
- initialization,
- interval type-2 fuzzy logic systems,
- Newton-Cotes quadrature formulas,
- reasonable initialization weighted EKM algorithms,
- simulations
Citation: Yang Chen, Jiaxiu Yang, Chenxi Li. Design of reasonable initialization weighted enhanced Karnik-Mendel algorithms for centroid type-reduction of interval type-2 fuzzy logic systems[J]. AIMS Mathematics, 2022, 7(6): 9846-9870. doi: 10.3934/math.2022549

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Abstract

Interval type-2 fuzzy logic systems (IT2 FLSs) already become an emerging technology in recent years. As the most popular type-reduction (TR) algorithms, Karnik-Mendel (KM) algorithms own the advantage of maintaining the uncertainties flow in systems. This paper analyzes the initialization for KM types of algorithms. Furthermore, the weighting approaches of them are also given by means of the Newton-Cotes quadrature formulas. Importantly, the reasonable initialization weighted enhanced Karnik-Mendel (RIWEKM) algorithms are provided to complete the centroid type-reduction of IT2 FLSs. Three computer simulation experiments illustrate that, the proposed RIWEKM algorithms own both smaller absolute errors and faster convergence speeds in contrast to the EKM and RIEKM algorithms.

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