Learning fuzzy cognitive maps with convergence using a multi-agent genetic algorithm

  • Ze Yang
  • Jing LiuEmail author
Methodologies and Application


Fuzzy cognitive maps (FCMs) are generally applied to model and analyze complex dynamical systems. Recently, many evolutionary-based algorithms are proposed to learn FCMs from historical data by optimizing Data_Error, which is used to evaluate the difference between available response sequences and generated response sequences. However, when Data_Error is adopted as the fitness function for learning FCMs, two problems arise. One is that the optimization reaches the desired result slowly; the other is that the learned FCMs have high link density. To solve these problems, we propose another objective named as convergence error, which is inspired by the convergence of FCMs, to evaluate the difference between the convergent value of available response sequences and that of generated response sequences. In addition, a multi-agent genetic algorithm (MAGA), which is effective for large-scale global numerical optimization, is adopted to optimize convergence error for learning FCMs. To this end, a novel learning approach, a multi-agent genetic algorithm based on the convergence error (MAGA-Convergence), is proposed for learning FCMs. MAGA-Convergence needs less data, because the only initial value and convergent value of the available response sequences are needed for learning FCMs. In the experiments, MAGA-Convergence is applied to learn the FCMs of synthetic data and the benchmarks DREAM3 and DREAM4 for gene regulatory network reconstruction. The experimental results show that the learned FCMs are sparse and could be learned in much fewer generations than other learning algorithms.


Fuzzy cognitive maps Convergence error Multi-agent genetic algorithm 



This work was supported in part by the General Program of National Natural Science Foundation of China (NSFC) under Grant 61773300 and in part by the Key Program of Fundamental Research Project of Natural Science of Shaanxi Province, China under Grant 2017JZ017.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Human and animal rights

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.Key Laboratory of Intelligent Perception and Image Understanding of Ministry of EducationXidian UniversityXi’anChina

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