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Enhancing the Expressive Power of Sugeno Integrals for Qualitative Data Analysis

  • Miguel CouceiroEmail author
  • Didier Dubois
  • Henri Prade
  • Agnès Rico
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 641)

Abstract

Sugeno integrals are useful for describing families of multiple criteria aggregation functions qualitatively. It is known that Sugeno integrals, as aggregation functions, can be represented by a set of rules. Each rule refers to the same threshold in the conditions about the values of the criteria and in the conclusion pertaining to the value of the integral. However, in the general case we expect rules where several thresholds appear. Some of these rules involving different thresholds can be represented by Sugeno utility functionals where criteria values are rescaled by means of utility functions associated with each criterion. But as shown in this paper, their representation power is quite restrictive. In contrast, we provide evidence to conjecture that the use of disjunctions or conjunctions of Sugeno integrals with utility functions drastically improves the expressive power and that they can capture any aggregation function on a finite scale, understood as piecewise unary aggregation functions.

Keywords

Sugeno integrals Piecewise unary functions Rule-based representation 

Notes

Acknowledgements

This work is supported by ANR-11-LABX-0040-CIMI (Centre International de Mathématiques et d’Informatique) within the program ANR-11-IDEX-0002-02, project ISIPA.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Miguel Couceiro
    • 1
    Email author
  • Didier Dubois
    • 2
  • Henri Prade
    • 2
  • Agnès Rico
    • 3
  1. 1.Université de Lorraine, LORIA, INRIA Nancy Grand-Est, CNRS, UMR 7503NancyFrance
  2. 2.IRIT-CNRSToulouseFrance
  3. 3.ERICUniversité de LyonLyonFrance

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