Top

Published in:

2019 | OriginalPaper | Chapter

Normed Utility Functions: Some Recent Advances

Authors : Radko Mesiar, Anna Kolesárová, Andrea Stupňanová, Ronald R. Yager

Published in: New Perspectives in Multiple Criteria Decision Making

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

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.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Preference Disaggregation for Multicriteria Decision Aiding: An Overview and Perspectives

next chapter Interpretation of Multicriteria Decision Making Models with Interacting Criteria

Beliakov, G., Pradera, A., & Calvo, T. (2007). Aggregation functions: A guide for practitioners. Heidelberg, Berlin, New York: Springer.

Beliakov, G., Bustince, H., & Calvo, T. (2016). A practical guide to averaging functions. Heidelberg, Berlin: Springer.CrossRef

Burkard, R. E., Dell’Amico, M., & Martello, S. (2009). Assignment problems: Revised reprint. Philadelphia (PA): SIAM. http://dx.doi.org/10.1137/1.9781611972238.

Bustince, H., Beliakov, G., Dimuro, G. P., Bedregal, B., & Mesiar, R. (2017). On the definition of penalty functions in data aggregation. Fuzzy Sets and Systems, 323, 1–18. https://doi.org/10.1016/j.fss.2016.09.011.

Calvo, T., & Beliakov, G. (2010). Aggregation functions based on penalties. Fuzzy Sets and Systems, 161(10), 1420–1436.CrossRef

Calvo, T., Kolesárová, A., Komorníková, M., & Mesiar, R. (2002). Aggregation operators: Properties, classes and construction methods. In: T. Calvo, G. Mayor, & R. Mesiar (Eds.), Aggregation operators. New trends and applications (pp. 3–107). Heidelberg: Physica-Verlag.

Calvo, T., Mesiar, R., & Yager, R. R. (2004). Quantitative weights and aggregation. IEEE Transactions on Fuzzy Systems, 12(1), 62–69.

Choquet, G. (1953). Theory of capacities. Annales de l’Institut Fourier, 5, 131–295.CrossRef

Daróczy, Z. (1972). Über eine Klasse von Mittelwerten. Publicationes Mathematicae Debrecen, 19, 211–217.

Decký, M., Mesiar, R., & Stupňanová, A. (2018). Deviation-based aggregation functions. Fuzzy Sets and Systems, 332, 29–36. https://doi.org/10.1016/j.fss.2017.03.016.

Durante, F., & Sempi, C. (2005). Semicopulae. Kybernetika, 41, 315–328.

Grabisch, M. (1997). \(k\)-order additive discrete fuzzy measures and their representation. Fuzzy Sets and Systems, 92, 167–189.CrossRef

Grabisch, M., Marichal, J. L., Mesiar, R., & Pap, E. (2009). Aggregation functions. Cambridge: Cambridge University Press.CrossRef

Greco, S., Ehrgott, M., & Figueira, J. R. (Eds.). (2010). Trends in multiple criteria decision analysis. Berlin: Springer.

Greco, S., Figueira, J. R., & Ehrgott, M. (Eds.). (2005). Multiple criteria decision analysis. Heidelberg: Springer.

Halaš, R., Mesiar, R., & Pócs, J. (2016). A new characterization of the discrete Sugeno integral. Information Fusion, 29, 84–86.

Klement, E. P., Mesiar, R., & Pap, E. (2010). A universal integral as common frame for Choquet and Sugeno integral. IEEE Transactions on Fuzzy Systems, 18, 178–187.CrossRef

Kolesárová, A., Li, J., & Mesiar, R. (2016). On \(k\)-additive aggregation functions. In: V. Torra, Y. Narukawa, G. Navarro-Arribas, & C. Yanez (Eds.), Modeling decisions for artificial intelligence. MDAI 2016. Lecture Notes in Computer Science (Vol. 9880, pp. 47–55). Springer.

Kolesárová, A., Li, J., & Mesiar, R. (2016). \(k\)-additive aggregation functions and their characterization. European Journal of Operational Research (submitted).

Losonczi, L. (1973). General inequalities of nonsymmetric means. Aequationes Mathematicae, 9, 221–235.CrossRef

Lovász, L. (1983). Submodular function and convexity. In Mathematical programming: The state of the art (pp. 235–257). Berlin: Springer.

Mesiar, R. (1997). \(k\)-order pan-additive discrete fuzzy measures. In 7th IFSA World Congress, June 1997, Prague, Czech Republic (pp. 488–490).

Mesiar, R. (2003). k-order additivity and maxitivity. Atti del Seminario Matematico e Fisico dell’Universita di Modena, 23(51), 179–189.

Mesiar, R., & Kolesárová, A. (2016). \(k\)-maxitive aggregation functions. Fuzzy Sets and Systems (submitted).

Mesiar, R., Stupňanová, A., & Yager, R. R. (2018). Extremal symmetrization of aggregation functions. Annals of Operations Research, 269, 535–548. https://doi.org/10.1007/s10479-017-2471-x.

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

Shilkret, N. (1971). Maxitive measure and integration. Indagationes Mathematicae, 33, 109–116.CrossRef

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

Valášková, L. (2007). Non-additive measures and integrals. Ph.D. thesis, STU Bratislava.

Yager, R. R. (1988). On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Transactions on Systems, Man and Cybernetics, 18, 183–190.CrossRef

Yager, R. R. (1993). Toward a general theory of information aggregation. Information Sciences, 68(3), 191–206.CrossRef

Zadeh, L. A. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1, 3–28.CrossRef

Title: Normed Utility Functions: Some Recent Advances
Authors: Radko Mesiar
Anna Kolesárová
Andrea Stupňanová
Ronald R. Yager
Publisher: Springer International Publishing
Book: New Perspectives in Multiple Criteria Decision Making
Print ISBN: 978-3-030-11481-7

Electronic ISBN: 978-3-030-11482-4

Copyright Year: 2019
DOI: https://doi.org/10.1007/978-3-030-11482-4_5