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Characterization of k-Choquet Integrals
2018In the present paper we characterize the class of all n-ary k-Choquet integrals and we find a minimal subset of points in the unit hypercube, the values on which fully determine the k-Choquet integral.
Lubomíra Horanská, Zdenko Takác
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On Choquet Integral Risk Measures
2010This paper aims at presenting the state-of-the-art of Choquet integral in quantifying the uncertainty in financial economics. Not only Choquet integral becomes a suitable model for defining financial coherent risk measures in the investment context, it seems also possible to use Choquet integral calculations as a means for asset pricing.We address also
Hung T. Nguyen 0002 +1 more
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The Choquet integral in Riesz space
Fuzzy Sets and Systems, 2008The author develops a theory of Choquet integration with respect to a Riesz space-valued non-additive measure. In particular, several convergence theorems are proved. Moreover, in an appendix is given an overview of the theory of Riemann-Stieltjes integration in Riesz spaces.
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Distances defined by Choquet integral
2007 IEEE International Fuzzy Systems Conference, 2007Some important inequalities in functional analysis are shown for the non-additive measure theory. As an application of the inequalities, the distances between fuzzy sets, which are generalisations of well-known distances, are introduced.
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Choquet Integration on Set Systems
2010We present a framework for a general Choquet integral on systems F of measurable sets relative to a finite universeNthat do not necessarily include all nonempty subsets. In this context, many functions become nonmeasurable, and the classical Choquet integral does not apply.
Faigle, Ulrich +2 more
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Robust optimization of the Choquet integral
Fuzzy Sets and Systems, 2013We study the problem of the Choquet integral maximization for the case when preferences of the decision maker do not define a unique capacity but rather some convex set. We introduce a robust version of the problem based on the minimax-regret criterion and construct a global optimization algorithm.
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On Some Generalizations of the Choquet Integral
2019In the present paper we survey several generalizations of the discrete Choquet integrals and we propose and study a new one. Our proposal is based on the Lovasz extension formula, in which we replace the product operator by some binary function F obtaining a new n-ary function \(\mathfrak {I}^F_{m}\).
Humberto Bustince +4 more
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Indices for Introspection on the Choquet Integral
2014Fuzzy measures (FMs) encode the worth (or importance) of different subsets of information sources in the fuzzy integral (FI). It is well-known that the Choquet FI (CFI) often reduces to an elementary aggregation operator for different selections of the FM.
Stanton R. Price +4 more
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Choquet Integral Models with a Constant
2010Choquet integral models are useful comprehensive evaluation models including interaction effects among evaluation items. Introducing a constant, Choquet integral model enables to change evaluation attitudes at the constant. In this paper, monotonicity and normality are defined for the model.
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