On Some Properties of Aggregation-Based Extensions of Fuzzy Measures

L’ubomíra Horanská

doi:10.2478/tmmp-2018-0020

.blurhash-client-img { display: none !important; }

On Some Properties of Aggregation-Based Extensions of Fuzzy Measures

Tatra Mountains Mathematical Publications

Volume 72 (2018): Issue 1 (December 2018)

By: L’ubomíra Horanská

Open Access

|Mar 2019

Abstract

In this paper, we analyse properties of aggregation-based extensions of fuzzy measures depending on properties of aggregation functions which they are based on. We mainly focus on properties possessed by the well-known Lovász and Owen extensions. Moreover, we characterize aggregation functions suitable for extension of particular subclasses of fuzzy measures.

References

[1] GRABISCH, M.: k-order additive discrete fuzzy measures and their representation, Fuzzy Sets and Systems 92 (1997), 167–189.10.1016/S0165-0114(97)00168-1
Search in Google Scholar Back to article
[2] GRABISCH, M.—MARICHAL, J.-L.—MESIAR, R.—PAP, E.: Aggregation Functions. Cambridge University Press, Cambridge, 2009.10.1017/CBO9781139644150
Search in Google Scholar Back to article
[3] KOLESÁROVÁ, A.—LI, J.—MESIAR, R.: k-additive aggregation functions and their characterization, European J. Oper. Res. 265 (2018), 985–992.10.1016/j.ejor.2017.08.036
Search in Google Scholar Back to article
[4] KOLESÁROVÁ, A.—STUPŇANOVÁ, A.—BEGANOVÁ, J.: Aggregation-based extensions of fuzzy measures, Fuzzy Sets and Systems 194 (2012), 1–14.10.1016/j.fss.2011.11.003
Search in Google Scholar Back to article
[5] LOVÁSZ, L.: Submodular function and convexity. In: Mathematical Programming: The State of the Art, 11th Int. Symp., Bonn, 1982 (A. Bachem et al., eds.), Springer, Berlin, 1983, pp. 235–257.10.1007/978-3-642-68874-4_10
Search in Google Scholar Back to article
[6] NELSEN, R. B.: An Introduction to Copulas. In: Lecture Notes in Statist., Vol. 139, Springer-Verlag, New York, 1999.10.1007/978-1-4757-3076-0
Search in Google Scholar Back to article
[7] OWEN, G.: Multilinear extensions of games, In: The Shapley Value (A. E. Roth, ed.), Essays in Honour of Lloyd S. Shapley, Cambridge University Press, 1988, pp. 139–151.10.1017/CBO9780511528446.011
Search in Google Scholar Back to article
[8] SPIZZICHINO, F. L.: On the probabilistic meaning of copula-based extensions of fuzzy measures. Applications to target-based utilities and multi-state reliability systems, Fuzzy Sets and Systems 354 (2019), 1–19.10.1016/j.fss.2018.01.011
Search in Google Scholar Back to article
[9] WANG, Z.—KLIR, G. J.: Fuzzy Measure Theory. Plenum Press, New York, 1992.10.1007/978-1-4757-5303-5
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2018-0020 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

Journal RSS Feed

Language: English

Page range: 43 - 54

Submitted on: Sep 14, 2018

Published on: Mar 12, 2019

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

aggregation function,

Related subjects:

© 2019 L’ubomíra Horanská, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 72 (2018): Issue 1 (December 2018)