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Normed Utility Functions: Some Recent Advances

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New Perspectives in Multiple Criteria Decision Making

Part of the book series: Multiple Criteria Decision Making ((MCDM))

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Abstract

In this chapter, we summarize some new results and trends in aggregation theory, thus contributing to the domain of normed utility functions. In particular, we discuss k-additive and k-maxitive aggregation functions and also present some construction methods. Penalty- and deviation-based approaches can be seen as implicitly given construction methods. For non-symmetric (weighted) aggregation functions, four symmetrization methods based on the optimization are introduced. All discussed results and construction methods are exemplified.

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Acknowledgements

The authors kindly acknowledge the support of the project of Science and Technology Assistance Agency under the contract No. APVV–14–0013 and the support of VEGA projects 1/0682/16 and 1/0614/18. Moreover, the work of R. Mesiar on this paper was supported by the NPUII project LQ1602 and Ronald R. Yager was supported by the Office of Navel Research.

Author information

Authors and Affiliations

  1. Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Radlinského 11, 810 05, Bratislava, Slovakia

    Radko Mesiar & Andrea Stupňanová

  2. Institute for Research and Applications of Fuzzy Modelling, University of Ostrava, 30. dubna 22, Ostrava, Czech Republic

    Radko Mesiar

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

    Anna Kolesárová

  4. Machine Intelligence Institute, Iona College, New Rochelle, NY, 10805, USA

    Ronald R. Yager

Authors
  1. Radko Mesiar
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  2. Anna Kolesárová
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  3. Andrea Stupňanová
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  4. Ronald R. Yager
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Corresponding author

Correspondence to Radko Mesiar .

Editor information

Editors and Affiliations

  1. School of Production Engineering and Management, Technical University of Crete, Chania, Greece

    Michalis Doumpos

  2. CEG-IST, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal

    José Rui Figueira

  3. Department of Economics and Business, University of Catania, Catania, Italy

    Salvatore Greco

  4. School of Production Engineering and Management, Technical University of Crete, Chania, Greece

    Constantin Zopounidis

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Mesiar, R., Kolesárová, A., Stupňanová, A., Yager, R.R. (2019). Normed Utility Functions: Some Recent Advances. In: Doumpos, M., Figueira, J., Greco, S., Zopounidis, C. (eds) New Perspectives in Multiple Criteria Decision Making. Multiple Criteria Decision Making. Springer, Cham. https://doi.org/10.1007/978-3-030-11482-4_5

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