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On k-\(\oplus \)-additive Aggregation Functions

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Modeling Decisions for Artificial Intelligence (MDAI 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11144))

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Abstract

To generalize the concept of k-maxitivity and k-additivity, we introduce k-\(\oplus \)-additive aggregation functions. We also characterize this kind of aggregation functions under some special conditions. Several examples are given to illustrate the new definitions.

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References

  1. Choquet, G.: Theory of capacities. Ann. Inst. Fourier. 5, 131–295 (1953)

    Article  MathSciNet  Google Scholar 

  2. Grabisch, M.: k-order additive discrete fuzzy measures and their representation. Fuzzy Sets Syst. 92, 167–189 (1997)

    Article  MathSciNet  Google Scholar 

  3. Grabisch, M., Marichal, J.L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, Cambridge (2009)

    Book  Google Scholar 

  4. Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer, Dordrecht (2000)

    Book  Google Scholar 

  5. Kolesárová, A., Li, J., Mesiar, R.: k-additive aggregation functions and their characterization. Eur. J. Operat. Res. 265, 985–992 (2018)

    Article  MathSciNet  Google Scholar 

  6. Mesiar, R.: k-order pan-discrete fuzzy measures. In: 7th IFSA World Congress, Prague, pp. 488–490 (1997)

    Google Scholar 

  7. Mesiar, R., Kolesárová, A.: k-maxitive aggregation functions. Fuzzy Sets Syst. 346, 127–137 (2018). https://doi.org/10.1016/j.fss.2017.12.016

    Article  MathSciNet  MATH  Google Scholar 

  8. Owen, G.: Multilinear extensions of games. In: Roth, A.E. (ed.) The Shapley value. Essays in Honour of Lloyd S. Shapley, pp. 139–151. Cambridge University Press (1988)

    Google Scholar 

  9. Shilkret, N.: Maxitive measure and integration. Indag. Math. 33, 109–116 (1971)

    Article  MathSciNet  Google Scholar 

  10. Sugeno, M., Murofushi, T.: Pseudo-additive measures and integrals. J. Math. Anal. Appl. 122, 197–222 (1987)

    Article  MathSciNet  Google Scholar 

  11. Sugeno, M.: Theory of fuzzy integrals and its applications. Ph.D. thesis, Tokyo Institute of Technology (1974)

    Google Scholar 

  12. Weber, S.: \(\perp \)-decomposable measures integrals for Archimedean \(t\)-conorms \( \perp \). J. Math. Anal. Appl. 101, 114–138 (1984)

    Article  MathSciNet  Google Scholar 

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Acknowledgment

The work on this contribution was supported by the grants APVV-14-0013 and APVV-17-0066. Fateme Kouchakinejad kindly acknowledges the support from Iran National Science Foundation: INSF.

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Authors and Affiliations

  1. Department of Statistics, Faculty of Mathematics and Computer Science, Shahid Bahonar University of Kerman, Kerman, Iran

    Fateme Kouchakinejad

  2. Institute of Information Engineering, Automation and Mathematics, Faculty of Chemical and Food Technology, Slovak University of Technology, Radlinského 9, 812 37, Bratislava, Slovakia

    Anna Kolesárová

  3. Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05, Bratislava, Slovakia

    Radko Mesiar

Authors
  1. Fateme Kouchakinejad
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  2. Anna Kolesárová
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  3. Radko Mesiar
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Corresponding author

Correspondence to Fateme Kouchakinejad .

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Editors and Affiliations

  1. Maynooth University, Maynooth, Ireland

    Vicenç Torra

  2. Department Management Science, Tamagawa University, Tokyo, Japan

    Yasuo Narukawa

  3. University of the Balearic Islands, Palma de Mallorca, Spain

    Isabel AguilĂł

  4. University of the Balearic Islands, Palma de Mallorca, Baleares, Spain

    Manuel González-Hidalgo

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Kouchakinejad, F., Kolesárová, A., Mesiar, R. (2018). On k-\(\oplus \)-additive Aggregation Functions. In: Torra, V., Narukawa, Y., Aguiló, I., González-Hidalgo, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2018. Lecture Notes in Computer Science(), vol 11144. Springer, Cham. https://doi.org/10.1007/978-3-030-00202-2_3

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  • DOI: https://doi.org/10.1007/978-3-030-00202-2_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00201-5

  • Online ISBN: 978-3-030-00202-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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