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Aggregation Functions With Non-Monotonic Measures

Author

Listed:
  • Cardin, Marta
  • Giove, Silvio

    (University of Venice)

Abstract

In this paper non-monotonic measures and their properties are considered and described. Subsequently we study discrete non-monotonic Choquet integral under the viewpoint of aggregation, and its axiomatic characterization. Moreover, we show that for non-monotonic measures the Shapley index can fail to represent the relative importance of a criterion, thus we introduce a new performance index. Finally we apply non-monotonic integral to a well known classical case study.

Suggested Citation

  • Cardin, Marta & Giove, Silvio, 2008. "Aggregation Functions With Non-Monotonic Measures," Fuzzy Economic Review, International Association for Fuzzy-set Management and Economy (SIGEF), vol. 0(2), pages 3-15, November.
  • Handle: RePEc:fzy:fuzeco:v:xiii:y:2008:i:2:p:3-15
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    Cited by:

    1. Silvia Bortot & Mario Fedrizzi & Silvio Giove, 2011. "Modelling fraud detection by attack trees and Choquet integral," DISA Working Papers 2011/09, Department of Computer and Management Sciences, University of Trento, Italy, revised 31 Aug 2011.

    More about this item

    Keywords

    aggregation operators; non-additive measures; non-monotonic measures; Choquet integral;

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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