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A Universal Integral
A Universal Integral,Erichpeter Klement,Radko Mesiar,Endre Pap
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A Universal Integral
(
Citations: 11
)
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Erichpeter Klement
,
Radko Mesiar
,
Endre Pap
Conference:
European Society for Fuzzy Logic and Technology  EUSFLAT
, pp. 253256, 2007
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www.informatik.unitrier.de
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Citation Context
(7)
...Accordingly, Sugeno and Choquet integrals on the scale [0, 1] are often called fuzzy integrals [19], [45] (see also [
36
])...
ErichPeter Klement
,
et al.
A Universal Integral as Common Frame for Choquet and Sugeno Integral
...Remark 2.5: Sugeno and Choquet integrals on the scale [0, 1] are often called fuzzy integrals [20], [46] (see also [
36
])...
Erich Peter Klement
,
et al.
A concept of universal integral based on measures of level sets
...In [
8
] the notion of a general integral was introduced...
Slavka Bodjanova
,
et al.
Selfduality of fuzzy integralbased TL and SLevaluators
...Most of the studies of nonadditive set functions and integrals have been focused to the case when their values are in nonnegative interval (fuzzy measures), e.g., [0, 1]. The fuzzy measure m : A→ [0, 1] (or [0, ∞]), m(∅ )=0 is a nondecreasing set function, defined on σalgebra A. Integrals can be viewed as an extension of underlining measures, see [6], [
7
]...
...The construction of general fuzzy integrals has been studied in [2], [
7
], [20]...
B. Mihailovic
,
et al.
Nonmonotonic set functions and general fuzzy integrals
...Accordingly, Sugeno and Choquet integrals on the scale [0, 1] are often called fuzzy integrals [19, 47] (see also [
37
])...
...sing and has 0 as neutral element (then the commutativity of ⊕ follows, see [
35
]), and which is leftdistributive with respect to ⊗, i.e., for all a, b, c ∈ [0, ∞] we have (a ⊕ b) ⊗ c =( a ⊗ c) ⊕(b ⊗ c). The pair (⊕, ⊗) is then called an integral operation pair...
...mutative, then it is called a triangular norm (tnorm for short, see [45, 59] and also [1,
35
, 60])...
Erich Peter Klement
,
et al.
A Nonlinear Integral Which Generalizes Both the Choquet and the Sugeno...
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Citations
(11)
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
Criteria satisfaction under measure based uncertainty
(
Citations: 1
)
Ronald R. Yager
Journal:
Fuzzy Optimization and Decision Making  FUZZY OPTIM DECIS MAK
, vol. 9, no. 3, pp. 307331, 2010
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
A concept of universal integral based on measures of level sets
Erich Peter Klement
,
Radko Mesiar
,
Endre Pap
Conference:
International Symposium on Intelligent Systems and Informatics  SISY
, 2009