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Normed Utility Functions: Some Recent Advances

  • Radko MesiarEmail author
  • Anna Kolesárová
  • Andrea Stupňanová
  • Ronald R. Yager
Chapter
Part of the Multiple Criteria Decision Making book series (MCDM)

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.

Notes

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.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Radko Mesiar
    • 1
    • 2
    Email author
  • Anna Kolesárová
    • 3
  • Andrea Stupňanová
    • 1
  • Ronald R. Yager
    • 4
  1. 1.Faculty of Civil EngineeringSlovak University of Technology in BratislavaBratislavaSlovakia
  2. 2.Institute for Research and Applications of Fuzzy ModellingUniversity of OstravaOstravaCzech Republic
  3. 3.Faculty of Chemical and Food Technology, Institute of Information Engineering, Automation and MathematicsSlovak University of Technology in BratislavaBratislavaSlovakia
  4. 4.Machine Intelligence InstituteIona CollegeNew RochelleUSA

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