A Note on Decomposition Integrals (original) (raw)

Abstract

Based on the idea of the decomposition integral proposed by Event and Lehrer, we introduce a new type of integrals. Moreover, we study the classes of measures turning inequalities (or incomparability) between special integrals such as Shilkret, Choquet, concave etc. integrals, into equalities.

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References

  1. Choquet, G.: Theory of capacities. Ann. Inst. Fourier 5, 131–295 (1955)
    Article MathSciNet Google Scholar
  2. Event, Y., Lehrer, E.: Decomposition-Integral: Unifying Choquet and the Concave Integrals, working paper
    Google Scholar
  3. Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation functions. Cambridge University Press, Cambridge (2009)
    MATH Google Scholar
  4. Klement, E.P., Mesiar, R., Pap, E.: A universal integral as common frame for Choquet and Sugeno integral. IEEE Transactions on Fuzzy Systems 18, 178–187 (2010)
    Article Google Scholar
  5. Lehrer, E.: A new integral for capacities. Economic Theory 39, 157–176 (2009)
    Article MathSciNet MATH Google Scholar
  6. Lin, T.Y.: Belief functions and probability for general spaces. In: 2011 IEEE Int. Conference on Granular Computing, pp. 314–319 (2010)
    Google Scholar
  7. Shilkret, N.: Maxitive measure and integration. Indag. Math. 33, 109–116 (1971)
    MathSciNet Google Scholar
  8. Yang, Q.: The Pan-integral on the Fuzzy Measure Space. Fuzzy Mathematics 3, 107–114 (1985)
    Google Scholar

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Authors and Affiliations

  1. Department of Mathematics, Slovak University of Technology, Radlinského 11, 813 68, Bratislava, Slovak Republic
    Andrea Stupňanová

Editor information

Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy
    Salvatore Greco & Benedetto Matarazzo &
  2. CNRS UMR 7606, DAPA, LIP6 8, Université Pierre et Marie Curie - Paris6, rue du Capitaine Scott, F-75015, Paris, France
    Bernadette Bouchon-Meunier
  3. Dip. Matematica e Informatica, Università di Perugia, 06123, Perugia, Italy
    Giulianella Coletti
  4. Department of Computer and Management Science, University of Trento, Via Inama 5, 38122, Trento, Italy
    Mario Fedrizzi
  5. Machine Intelligence Institute — IONA College,, 10801, New Rochelle, NY, USA
    Ronald R. Yager

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© 2012 Springer-Verlag Berlin Heidelberg

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Stupňanová, A. (2012). A Note on Decomposition Integrals. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31724-8\_57

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