Probability inequalities for decomposition integrals

Agahi, Hamzeh; Mesiar, Radko

doi:10.1016/j.cam.2016.11.014

Cited by 5 publications

(2 citation statements)

References 39 publications

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“…The decomposition integral forms a general setting for these nonlinear integrals (see also [2,3]). In recent years, decomposition integrals have attracted more and more attention from researchers, and a lot of results have been obtained (see [2][3][4][5][6][7][8][9][10][11][12]).…”

Section: Introductionmentioning

confidence: 99%

Decomposition Integrals of Set-Valued Functions Based on Fuzzy Measures

2023

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The decomposition integrals of set-valued functions with regards to fuzzy measures are introduced in a natural way. These integrals are an extension of the decomposition integral for real-valued functions and include several types of set-valued integrals, such as the Aumann integral based on the classical Lebesgue integral, the set-valued Choquet, pan-, concave and Shilkret integrals of set-valued functions with regard to capacity, etc. Some basic properties are presented and the monotonicity of the integrals in the sense of different types of the preorder relations are shown. By means of the monotonicity, the Chebyshev inequalities of decomposition integrals for set-valued functions are established. As a special case, we show the linearity of concave integrals of set-valued functions in terms of the equivalence relation based on a kind of preorder. The coincidences among the set-valued Choquet, the set-valued pan-integral and the set-valued concave integral are presented.

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Section: Introductionmentioning

confidence: 99%

Decomposition Integrals of Set-Valued Functions Based on Fuzzy Measures

2023

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“…For example, Agahi et al [1][2][3] presented some interesting extensions of Hölder's inequality (1) for decomposition integral, Sugeno integral, and pseudo-integral. Benmerrouche et al [4] obtained a new technique based on Hölder's integral inequality (1) which provides fundamental constraints on the QCD sum-rules.…”

Section: Introductionmentioning

confidence: 99%