Soft Computing

, Volume 11, Issue 11, pp 1013–1031 | Cite as

A Pareto-based multi-objective evolutionary approach to the identification of Mamdani fuzzy systems

  • Marco Cococcioni
  • Pietro Ducange
  • Beatrice Lazzerini
  • Francesco MarcelloniEmail author
Original Paper


In the last years, the numerous successful applications of fuzzy rule-based systems (FRBSs) to several different domains have produced a considerable interest in methods to generate FRBSs from data. Most of the methods proposed in the literature, however, focus on performance maximization and omit to consider FRBS comprehensibility. Only recently, the problem of finding the right trade-off between performance and comprehensibility, in spite of the original nature of fuzzy logic, has arisen a growing interest in methods which take both the aspects into account. In this paper, we propose a Pareto-based multi-objective evolutionary approach to generate a set of Mamdani fuzzy systems from numerical data. We adopt a variant of the well-known (2+2) Pareto Archived Evolutionary Strategy ((2+2)PAES), which adopts the one-point crossover and two appropriately defined mutation operators. (2+2)PAES determines an approximation of the optimal Pareto front by concurrently minimizing the root mean squared error and the complexity. Complexity is measured as sum of the conditions which compose the antecedents of the rules included in the FRBS. Thus, low values of complexity correspond to Mamdani fuzzy systems characterized by a low number of rules and a low number of input variables really used in each rule. This ensures a high comprehensibility of the systems. We tested our version of (2+2)PAES on three well-known regression benchmarks, namely the Box and Jenkins Gas Furnace, the Mackey-Glass chaotic time series and Lorenz attractor time series datasets. To show the good characteristics of our approach, we compare the Pareto fronts produced by the (2+2)PAES with the ones obtained by applying a heuristic approach based on SVD-QR decomposition and four different multi-objective evolutionary algorithms.


Root Mean Square Error Fuzzy Rule Pareto Front Multiobjective Evolutionary Algorithm Strength Pareto Evolutionary Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Marco Cococcioni
    • 1
  • Pietro Ducange
    • 1
  • Beatrice Lazzerini
    • 1
  • Francesco Marcelloni
    • 1
    Email author
  1. 1.Dipartimento di Ingegneria dell’Informazione: Elettronica, Informatica, TelecomunicazioniUniversity of PisaPisaItaly

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