Context adaptation of fuzzy systems through a multi-objective evolutionary approach based on a novel interpretability index

  • Authors:

  • Alessio Botta;Beatrice Lazzerini;Francesco Marcelloni;Dan C. Stefanescu

  • Affiliations:

  • IMT Lucca Institute for Advanced Studies, Piazza San Ponziano 6, 55100, Lucca, Italy;University of Pisa, Dipartimento di Ingegneria dell’Informazione: Elettronica, Informatica, Telecomunicazioni, via Diotisalvi 2, 56122, Pisa, Italy;University of Pisa, Dipartimento di Ingegneria dell’Informazione: Elettronica, Informatica, Telecomunicazioni, via Diotisalvi 2, 56122, Pisa, Italy;Suffolk University, Mathematics and Computer Science Department, Beacon Hill, Boston, MA, USA

  • Venue:
  • Soft Computing - A Fusion of Foundations, Methodologies and Applications - Genetic Fuzzy Systems: Recent Developments and Future Directions; Guest editors: Jorge Casillas, Brian Carse
  • Year:
  • 2008

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Abstract

Context adaptation (CA) based on evolutionary algorithms is certainly a promising approach to the development of fuzzy rule-based systems (FRBSs). In CA, a context-free model is instantiated to a context-adapted FRBS so as to increase accuracy. A typical requirement in CA is that the context-adapted system maintains the same interpretability as the context-free model, a challenging constraint given that accuracy and interpretability are often conflicting objectives. Furthermore, interpretability is difficult to quantify because of its very nature of being a qualitative concept. In this paper, we first introduce a novel index based on fuzzy ordering relations in order to provide a measure of interpretability. Then, we use the proposed index and the mean square error as goals of a multi-objective evolutionary algorithm aimed at generating a set of Pareto-optimum context-adapted Mamdani-type FRBSs with different trade-offs between accuracy and interpretability. CA is obtained through the use of specifically designed operators that adjust the universe of the input and output variables, and modify the core, the support and the shape of fuzzy sets characterizing the partitions of these universes. Finally, we show results obtained by using our approach on synthetic and real data sets.