Hierarchical fuzzy design by a multi-objective evolutionary hybrid approach

  • Yosra JarrayaEmail author
  • Souhir Bouaziz
  • Adel M. Alimi
  • Ajith Abraham
Methodologies and Application


This paper presents a new tree hierarchical representation of type-2 fuzzy systems. The proposed system is called the type-2 hierarchical flexible beta fuzzy system (T2HFBFS) and is trained based on two-phase optimization mechanism. The first optimization step is a multi-objective structural learning phase. This phase is based on the multi-objective extended immune programming algorithm and aims to obtain an improved T2HFBFS structure with good interpretability-accuracy trade-off. The second optimization step is a parameter tuning phase. Using a hybrid evolutionary algorithm, this phase allows the adjustment of antecedent and consequent membership function parameters of the obtained T2HFBFS. By interleaving the two learning steps, an optimal and accurate hierarchical type-2 fuzzy system is derived with the least number of possible rules. The performance of the system is evaluated by conducting case studies for time series prediction problems and high-dimensional classification problems. Results prove that the T2HFBFS could attain superior performance than other existing approaches in terms of achieving high accuracy with a significant rule reduction.


Hierarchical design Type-2 fuzzy systems Beta basis function Structure learning Multi-objective optimization Parameter tuning 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Research Groups in Intelligent Machines (REGIM-Lab), National School of Engineers (ENIS)University of SfaxSfaxTunisia
  2. 2.Machine Intelligence Research Labs (MIR Labs)AuburnUSA
  3. 3.IT4InnovationsVSB-Technical University of OstravaOstravaCzech Republic

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