Characterization of decomposition integrals extending Lebesgue integral

Li, Jun; Mesiar, Radko; Ouyang, Yao; Šeliga, Adam

doi:10.1016/j.fss.2021.04.015

Cited by 5 publications

(2 citation statements)

References 12 publications

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“…Or, is it possible to characterize those decomposition systems for which the lower convolution of sub-decomposition integrals is again a sub-decomposition integral (in the spirit of Example 4)? Another interesting question is related to the fact that some decomposition integrals are extensions of the Lebesgue integral (i.e., for additive monotone measures, they coincide with the Lebesgue integral); for more details, see [14]. Now, we have the problem of how our proposed convolutions are related to the standard convolution based on the Lebesgue integral.…”

Section: Discussionmentioning

confidence: 99%

Convolution of Decomposition Integrals

Šeliga

2022

Mathematics

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Four different types of convolutions of aggregation functions (the upper, the lower, the super-, and the sub-convolution) are examined in the setting of both sub- and super-decomposition integrals defined on a finite space. Examples of the results of the paper are provided. As a by-product, the super-additive transformation of sub-decomposition integrals and the sub-additive transformation of super-decomposition integrals are fully characterized. Possible applications are indicated.

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Section: Discussionmentioning

confidence: 99%

Convolution of Decomposition Integrals

Šeliga

2022

Mathematics

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“…Note that the above discussions only concern two kinds of relations for decomposition systems from X: "⊆" and " ". There are also other preorders on the class of decomposition systems, see, e.g., [3,43,44]. Similarly, we can discuss the monotonicity of set-valued decomposition integrals in the sense of these preorders.…”

Section: G H Impliesmentioning

confidence: 98%

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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On the coincidence of measure-based decomposition and superdecomposition integrals

Mesiar

Ouyang

2023

Fuzzy Sets and Systems

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Characterization of decomposition integrals extending Lebesgue integral

Cited by 5 publications

References 12 publications

Convolution of Decomposition Integrals

Convolution of Decomposition Integrals

Decomposition Integrals of Set-Valued Functions Based on Fuzzy Measures

On the coincidence of measure-based decomposition and superdecomposition integrals

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