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Rule Base Reduction Using Conflicting and Reinforcement Measures

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Multidisciplinary Approaches to Neural Computing

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 69))

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Abstract

In this paper we present an innovative procedure to reduce the number of rules in a Mamdani rule-based fuzzy systems. First of all, we extend the similarity measure or degree between antecedent and consequent of two rules. Subsequently, we use the similarity degree to compute two new measures of conflicting and reinforcement between fuzzy rules. We apply these conflicting and reinforcement measures to suitably reduce the number of rules. Namely, we merge two rules together if they are redundant, i.e. if both antecedent and consequence are similar together, repeating this operation until no similar rules exist, obtaining a reduced set of rules. Again, we remove from the reduced set the rule with conflict with other, i.e. if antecedent are similar and consequence not; among the two, we remove the one characterized by higher average conflict with all the rules in the reduced set.

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Notes

  1. 1.

    A triangular fuzzy number is a sub-case of a trapezoidal one, with \(a_2=a_3\), while a bell-shape recalls a gaussian distribution.

  2. 2.

    Alternatively, in [9] the following merging procedure is proposed: if \(A=(a_1,a_2,a_3,a_4)\) and \(B=(b_1,b_2,b_3,b_4)\) are trapezoidal fuzzy numbers, the merged (trapezoidal) fuzzy number \(C=(c_1,c_2,c_3,c_4)\) is obtained by \(c_1=\min (a_1,b_1)\), \(c_2=\lambda _{2} a_2+(1-\lambda _{2}) b_2\), \(c_3=\lambda _{3} a_3+(1-\lambda _{3}) b_3\), \(c_4=\max (a_4,b_4)\), where \(\lambda _{2},\lambda _{3}\in [0,1]\).

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Author information

Authors and Affiliations

  1. Department of Management, Economics, Mathematics and Statistics, University of Salento, Lecce, Italy

    Luca Anzilli

  2. Department of Economics, University Ca’ Foscari of Venice, Venice, Italy

    Silvio Giove

Authors
  1. Luca Anzilli
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  2. Silvio Giove
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Correspondence to Luca Anzilli .

Editor information

Editors and Affiliations

  1. Dipartimento di Psicologia, Università della Campania “Luigi Vanvitelli”, Caserta, Italy

    Anna Esposito

  2. Fundació Tecnocampus, Pompeu Fabra University, Mataro, Spain

    Marcos Faudez-Zanuy

  3. Department of Civil, Environmental, Energy, and Material Engineering, Mediterranea University of Reggio Calabria, Reggio Calabria, Italy

    Francesco Carlo Morabito

  4. Dipartimento di Elettronica e Telecomunicazioni, Politecnico di Torino, Laboratorio di Neuronica, Torino, Italy

    Eros Pasero

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Anzilli, L., Giove, S. (2018). Rule Base Reduction Using Conflicting and Reinforcement Measures. In: Esposito, A., Faudez-Zanuy, M., Morabito, F., Pasero, E. (eds) Multidisciplinary Approaches to Neural Computing. Smart Innovation, Systems and Technologies, vol 69. Springer, Cham. https://doi.org/10.1007/978-3-319-56904-8_13

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  • DOI: https://doi.org/10.1007/978-3-319-56904-8_13

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  • Online ISBN: 978-3-319-56904-8

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