Soft Computing

, Volume 22, Issue 4, pp 1361–1380 | Cite as

Study on centroid type-reduction of general type-2 fuzzy logic systems with weighted enhanced Karnik–Mendel algorithms

  • Yang ChenEmail author
  • Dazhi Wang
Methodologies and Application


With the development of \(\alpha \)-planes representation of general type-2 fuzzy sets (GT2 FSs), general type-2 fuzzy logic systems (GT2 FLSs) based on GT2 FSs have become a hot topic in academic field. While type-reduction (TR) is most critical block for a T2 FLS, generally speaking, the most popular Karnik–Mendel (KM) or enhanced KM (EKM) algorithms are used to perform the TR. The paper connects the EKM and the continuous version of EKM algorithms together and expands the EKM algorithms to three different forms of weighted EKM (WEKM) algorithms resort to the Newton–Cotes quadrature formulas of numerical integration techniques, while the EKM algorithms just become a special case of the WEKM algorithms. Four computer simulation examples are used to illustrate the performances of the WEKM algorithms. Compared with the EKM algorithms, the WEKM algorithms have smaller absolute error and faster convergence speed to compute the centroid defuzzified value of GT2 FLSs in general, which make them potentially applicable for T2 FLSs designers and adopters.


General type-2 fuzzy logic systems \(\alpha \)-Planes Type-reduction Weighted enhanced Karnik–Mendel algorithms Continuous enhanced Karnik–Mendel algorithms Computer simulation 



This paper is partially sponsored by the Natural Science Foundation of China (No. 61374113) and Fundamental Research Funds for Liaoning’s Universities (No. JL201615410). The author is so thankful to Prof. J. M. Mendel, who has offered the author some worthy suggestions.

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.College of ScienceLiaoning University of TechnologyJinzhouChina
  2. 2.College of Information Science and EngineeringNortheastern UniversityShenyangChina

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