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Fusion functions based discrete Choquet-like integrals

Author

Listed:
  • Mesiar, R.
  • Kolesárová, A.
  • Bustince, H.
  • Dimuro, G.P.
  • Bedregal, B.C.

Abstract

In this paper, we generalize a formula for the discrete Choquet integral by replacing the standard product by a suitable fusion function. For the introduced fusion functions based discrete Choquet-like integrals we discuss and prove several properties and also show that our generalization leads to several new interesting functionals. We provide a complete characterization of the introduced functionals as aggregation functions. For n=2, several new aggregation functions are obtained, and if symmetric capacities are considered, our approach yields new generalizations of OWA operators. If n > 2, the introduced functionals are aggregation functions only if they are Choquet integrals with respect to some distorted capacity.

Suggested Citation

  • Mesiar, R. & Kolesárová, A. & Bustince, H. & Dimuro, G.P. & Bedregal, B.C., 2016. "Fusion functions based discrete Choquet-like integrals," European Journal of Operational Research, Elsevier, vol. 252(2), pages 601-609.
  • Handle: RePEc:eee:ejores:v:252:y:2016:i:2:p:601-609
    DOI: 10.1016/j.ejor.2016.01.027
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    References listed on IDEAS

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    1. Genest, C. & Quesada Molina, J. J. & Rodriguez Lallena, J. A. & Sempi, C., 1999. "A Characterization of Quasi-copulas," Journal of Multivariate Analysis, Elsevier, vol. 69(2), pages 193-205, May.
    2. Ehud Lehrer, 2009. "A new integral for capacities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(1), pages 157-176, April.
    3. Bustince, H. & Fernandez, J. & Kolesárová, A. & Mesiar, R., 2015. "Directional monotonicity of fusion functions," European Journal of Operational Research, Elsevier, vol. 244(1), pages 300-308.
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