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Multi-polar Aggregation

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Advances in Computational Intelligence (IPMU 2012)

Abstract

In this contribution we introduce a notion of an m-polar aggregation operator as a generalization of aggregation operators and bipolar aggregation operators, and we introduce the main properties of these aggregation operators. Extensions of some (bipolar) aggregation operators to m-polar aggregation operators are also introduced, as well as metrics on the category space K × [0,1] related to m-polar aggregation.

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References

  1. Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practitioners. Springer, New York (2007)

    Google Scholar 

  2. Calvo, T., Kolesárová, A., Komorníková, M., Mesiar, R.: Aggregation Operators: Properties, Classes and Construction Methods. In: Calvo, T., Mayor, G., Mesiar, R. (eds.) Aggregation Operators, pp. 3–107. Physica-Verlag, Heidelberg (2002)

    Google Scholar 

  3. Choquet, G.: Theory of capacities. Ann. Inst. Fourier 5, 131–295 (1953-1954)

    Google Scholar 

  4. Denneberg, D.: Non-additive Measure and Integral. Kluwer Academic Publishers, Dordrecht (1994)

    MATH  Google Scholar 

  5. Grabisch, M., De Baets, B., Fodor, J.: On symmetric pseudo-additions. In: Proc. IPMU 2002, Annecy, pp. 1349–1355 (2002)

    Google Scholar 

  6. Grabisch, M., Labreuche, C.: Bi-capacities for decision making on bipolar scales. In: Proc. EUROFUSE Workshop on Information Systems, Varenna, pp. 185–190 (2002)

    Google Scholar 

  7. Grabisch, M.: The symmetric Sugeno integral. Fuzzy Sets and Systems 139, 473–490 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. Grabisch, M.: The Mőbius function on symmetric ordered structures and its application to capacities on finite sets. Discrete Math 287(1-3), 17–34 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. Grabisch, M., Labreuche, C.: Capacities on lattices and k-ary capacities. In: Proc. EUSFLAT 2003, Zittau, Germany, pp. 304–307 (2003)

    Google Scholar 

  10. Grabisch, M., Labreuche, C.: Bipolarization of posets and natural interpolation. Journal of Mathematical Analysis and Application 343, 1080–1097 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge Univ. Press, Cambridge (2009)

    MATH  Google Scholar 

  12. Hájek, P., Havránek, T., Jiroušek, R.: Uncertain Information Processing in Expert Systems. CRC Press, Boca Raton (1992)

    Google Scholar 

  13. Mesiar, R., De Baets, B.: New Construction Methods for Aggregation operators. In: Proc. IPMU 2000, Madrid, pp. 701–707 (2000)

    Google Scholar 

  14. Mesiarová, A., Lazaro, J.: Bipolar Aggregation operators. In: Proc. AGOP 2003, pp. 119–123. Alcalá de Henares (2003)

    Google Scholar 

  15. Mesiarová-Zemánková, A., Mesiar, R., Ahmad, K.: The balancing Choquet integral. Fuzzy Sets and Systems 161(17), 2243–2255 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  16. Mesiarová-Zemánková, A., Ahmad, K.: Multi-polar Choquet integral. Fuzzy Sets and Systems (submitted)

    Google Scholar 

  17. Shortliffe, E.H.: Computer-Based Medical Consultations: MYCIN. Elsevier/North-Holland, Amsterdam (1976)

    Google Scholar 

  18. Pap, E.: Null-Additive Set Functions. Kluwer Academic Publishers, Dordrecht (1995)

    MATH  Google Scholar 

  19. Šipoš, J.: Integral with respect to a premeasure. Math. Slovaca 29, 141–145 (1979)

    MathSciNet  MATH  Google Scholar 

  20. Takahagi, E.: Choquet-Integral-Based Evaluations by Fuzzy Rules: Methods for Developing Fuzzy Rule Tables on the Basis of Weights and Interaction Degrees. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. CCIS, vol. 80, pp. 515–524. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  21. Takahagi, E.: Multiple-output Choquet integral models and their applications in classification methods. International Journal of Intelligent Technologies and Applied Statistics 4(4), 519–530 (2011)

    Google Scholar 

  22. Tversky, A., Kahneman, D.: Advances in prospect theory: cumulative representation of uncertainty. J. of Risk and Uncertainty (1992)

    Google Scholar 

  23. Yager, R., Rybalov, A.: Bipolar aggregation using the Uninorms. Fuzzy Optimization and Decision Making 10(1), 59–70 (2011)

    Article  MathSciNet  Google Scholar 

  24. Zhang, W.–R.: YinYang Bipolar T-norms and T-conorms as granular neurological operators. In: Proc. IEEE International Conference on Granular Computing, Atlanta, pp. 91–96 (2006)

    Google Scholar 

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Mesiarová-Zemánková, A., Ahmad, K. (2012). Multi-polar Aggregation. 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 299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31718-7_40

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  • DOI: https://doi.org/10.1007/978-3-642-31718-7_40

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31717-0

  • Online ISBN: 978-3-642-31718-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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