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Keywords
(4)
choquet integral
Fuzzy Integral
Fuzzy Measure
sugeno integral
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Fuzzy integrals and linearity
Fuzzy integrals and linearity,10.1016/j.ijar.2007.05.013,International Journal of Approximate Reasoning,Radko Mesiar,Andrea Mesiarová
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Fuzzy integrals and linearity
(
Citations: 19
)
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Radko Mesiar
,
Andrea Mesiarová
Linearity and generalized linearity of fuzzy integrals are studied. For continuous from below fuzzy integrals, linearity leads to the Lebesgue integral while the comonotone linearity results to the
Choquet integral
with respect to a selfdual
fuzzy measure
m. Similar results in the case of idempotent linearity are presented. Some open problems were stated, too. Finally, pseudolinearity related to two types of semirings is discussed.
Journal:
International Journal of Approximate Reasoning  IJAR
, vol. 47, no. 3, pp. 352358, 2008
DOI:
10.1016/j.ijar.2007.05.013
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Citation Context
(3)
...Clearly, we have Su = I Min and Sh = IProd , where the pseudomultiplications Min and Prod are given (as usual) by Min(a, b) = min(a, b) and Prod(a, b )= a · b. Note that, the nonlinearity of the Sugeno integral Su (see, e.g., [37], [
46
]) implies that universal integrals are also nonlinear, in general...
ErichPeter Klement
,
et al.
A Universal Integral as Common Frame for Choquet and Sugeno Integral
...It is well known that Sugeno integral is a type of nonlinear integral [
7
], i.e., for general case,...
H. RománFlores
,
et al.
Extended Chebyshev type inequality for Sugeno integral
...Clearly, we have Su = IMin and Sh = IProd, where the pseudomultiplications Min and Prod are given (as usual) by Min(a, b )= min(a, b) and Prod(a, b )= a · b. Note that the nonlinearity of the Sugeno integral Su (see, e.g., [38], [
47
]) implies that universal integrals are also nonlinear, in general...
Erich Peter Klement
,
et al.
A concept of universal integral based on measures of level sets
References
(13)
Pseudoarithmetical operations as a basis for the general measure and integration theory
(
Citations: 10
)
Pietro Benvenuti
,
Radko Mesiar
Journal:
Information Sciences  ISCI
, vol. 160, no. 14, pp. 111, 2004
Nonadditive Measure and Integral
(
Citations: 484
)
D. Denneberg
Published in 1994.
Fuzzy integrals based on pseudoadditions and multiplications
(
Citations: 12
)
H ICHIHASHI
,
H TANAKA
,
K ASAI
Journal:
Journal of Mathematical Analysis and Applications  J MATH ANAL APPL
, vol. 130, no. 2, pp. 354364, 1988
Homogeneity properties of seminormed fuzzy integrals
(
Citations: 2
)
Mi Hye Kim
Journal:
Fuzzy Sets and Systems  FSS
, vol. 157, no. 3, pp. 411426, 2006
Integration with Respect to Decomposable Measures, Based on a Conditionally Distributive Semiring on the Unit Interval
(
Citations: 12
)
ERICH PETER KLEMENT
,
Radko Mesiar
,
Endre Pap
Journal:
International Journal of Uncertainty, Fuzziness and Knowledgebased Systems  IJUFKS
, vol. 8, no. 6, pp. 701717, 2000
Sort by:
Citations
(19)
Generalized Lebesgue integral
(
Citations: 1
)
Qiang Zhang
,
Radko Mesiar
,
Jun Li
,
Peter Struk
Journal:
International Journal of Approximate Reasoning  IJAR
, vol. 52, no. 3, pp. 427443, 2011
General BarnesGodunovaLevin type inequalities for Sugeno integral
(
Citations: 1
)
Hamzeh Agahi
,
Heriberto RománFlores
,
A. FloresFranulic
Journal:
Information Sciences  ISCI
, vol. 181, no. 6, pp. 10721079, 2011
Effect of ω3 fatty acids on life span
Unknown
Journal:
Nutrition
, vol. 27, no. 3, pp. 333333, 2011
General Minkowski type inequalities for Sugeno integrals
(
Citations: 18
)
Hamzeh Agahi
,
Radko Mesiar
,
Yao Ouyang
Journal:
Fuzzy Sets and Systems  FSS
, vol. 161, no. 5, pp. 708715, 2010
A Universal Integral as Common Frame for Choquet and Sugeno Integral
(
Citations: 10
)
ErichPeter Klement
,
Radko Mesiar
,
Endre Pap
Journal:
IEEE Transactions on Fuzzy Systems  TFS
, vol. 18, no. 1, pp. 178187, 2010