On Some Properties of Aggregation-Based Extensions of Fuzzy Measures

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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.

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  • [1] GRABISCH M.: k-order additive discrete fuzzy measures and their representation Fuzzy Sets and Systems 92 (1997) 167–189.

  • [2] GRABISCH M.—MARICHAL J.-L.—MESIAR R.—PAP E.: Aggregation Functions. Cambridge University Press Cambridge 2009.

  • [3] KOLESÁROVÁ A.—LI J.—MESIAR R.: k-additive aggregation functions and their characterization European J. Oper. Res. 265 (2018) 985–992.

  • [4] KOLESÁROVÁ A.—STUPŇANOVÁ A.—BEGANOVÁ J.: Aggregation-based extensions of fuzzy measures Fuzzy Sets and Systems 194 (2012) 1–14.

  • [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.

  • [6] NELSEN R. B.: An Introduction to Copulas. In: Lecture Notes in Statist. Vol. 139 Springer-Verlag New York 1999.

  • [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.

  • [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.

  • [9] WANG Z.—KLIR G. J.: Fuzzy Measure Theory. Plenum Press New York 1992.

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