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Keywords
(6)
Aggregation Function
choquet integral
Cumulative Prospect Theory
Indexation
owa operator
sugeno integral
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The Choquet integral with respect to a level dependent capacity
The Choquet integral with respect to a level dependent capacity,10.1016/j.fss.2011.03.012,Fuzzy Sets and Systems,Salvatore Greco,Benedetto Matarazzo,S
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The Choquet integral with respect to a level dependent capacity
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Citations: 9
)
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Salvatore Greco
,
Benedetto Matarazzo
,
Silvio Giove
We present a generalization of
Choquet integral
in which the capacity depends also on the value of the aggregated variables. We show that as particular cases of our generalization of
Choquet integral
there are the Sugeno integral, the Šipoš integral and the
Cumulative Prospect Theory
functional. We also show that many concepts such as Möbius transform, importance index, interaction index, korder capacities and OWA operators, introduced in the research about Choquet integral, can be generalized in the considered context.
Journal:
Fuzzy Sets and Systems  FSS
, vol. 175, no. 1, pp. 135, 2011
DOI:
10.1016/j.fss.2011.03.012
Cumulative
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)
Citation Context
(5)
...Recently, in [3] the NAROR approach has been extended to some generalizations of the Choquet integrals specifically, bipolar Choquet integral (see [13], [14] and [17]), level dependent Choquet integral and bipolar level dependent Choquet integral (see [
10
].)...
Silvia Angilella
,
et al.
The Most Representative Utility Function for NonAdditive Robust Ordin...
...For the first time this idea was presented in [
4
]...
...This will lead to the notion of generalized capacity (this name was originally proposed in [
4
])...
Slavka Bodjanova
,
et al.
Sugeno and Shilkret integrals, and T and Sevaluators
...Definition 9 ([
7
]) Let us consider a set of criteria X = {1, 2,...,n}...
...Definition 10 ([
7
]) We define the leveldependent Choquet integral of a function f : X ! [0, 1] with respect to the generalized capacity µG as follows:...
Dana Hlinena
,
et al.
Choquet integral and its modifications
...Generalizing the idea presented in [
5
] we get the following definitions:...
Slavka Bodjanova
,
et al.
Selfduality of fuzzy integralbased TL and SLevaluators
...This problem can be solved using a socalled leveldependent Choquet integral, introduced by S. Greco, S. Giove and B. Matarazzo (see [
10
])...
...Definition 8. ( [
10
]) Let us consider a set of criteria X = {1, 2,..., m}. We define a generalized capacity as function μ G :2 X ×[0, 1] → [0, 1] such that...
...Definition 9. ( [
10
]) We define the leveldependent Choquet integral of a function f : X → [0, 1] with respect to the generalized capacity μ G as follows...
Martin Kalina
,
et al.
Preference Modelling Using the LevelDependent Choquet Integral with R...
References
(14)
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(
Citations: 19
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Silvia Angilella
,
Salvatore Greco
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,
Benedetto Matarazzo
Journal:
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On equivalence classes of fuzzy connectivesthe case of fuzzy integrals
(
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Michel Grabisch
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IEEE Transactions on Fuzzy Systems  TFS
, vol. 3, no. 1, pp. 96109, 1995
The application of fuzzy integrals in multicriteria decision making
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Michel Grabisch
Journal:
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korder additive discrete fuzzy measures and their representation
(
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Michel Grabisch
Journal:
Fuzzy Sets and Systems  FSS
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Citations
(9)
The Most Representative Utility Function for NonAdditive Robust Ordinal Regression
Silvia Angilella
,
Salvatore Greco
,
Benedetto Matarazzo
Conference:
Information Processing and Management of Uncertainty
, pp. 220229, 2010
Nonadditive Robust Ordinal Regression with Choquet integral, Bipolar and Level Dependent Choquet integrals
(
Citations: 2
)
Silvia Angilella
,
Salvatore Greco
,
Benedetto Matarazzo
Conference:
European Society for Fuzzy Logic and Technology  EUSFLAT
, pp. 11941199, 2009
LevelDependent Sugeno Integral
(
Citations: 1
)
Radko Mesiar
,
A. Mesiarovázemenkova
,
Khurshid Ahmad
Journal:
IEEE Transactions on Fuzzy Systems  TFS
, vol. 17, no. 1, pp. 167172, 2009
Universal Integrals Based on Level Dependent Capacities
Erichpeter Klement
,
Anna Kolesárová
,
Radko Mesiar
,
Andrea Stupnanová
Conference:
European Society for Fuzzy Logic and Technology  EUSFLAT
, pp. 114118, 2009
Sugeno and Shilkret integrals, and T and Sevaluators
Slavka Bodjanova
,
Martin Kalina
Conference:
International Symposium on Intelligent Systems and Informatics  SISY
, 2009