Asymmetric integral as a limit of generated Choquet integrals based on absolutely monotone real set functions

2011 ◽  
Vol 181 (1) ◽  
pp. 39-49 ◽  
Author(s):  
Biljana Mihailović ◽  
Endre Pap
Keyword(s):  
Set Functions ◽  
Choquet Integrals ◽  
Absolutely Monotone

scholarly journals Quantitative estimates in uniform and pointwise approximation by Bernstein-Durrmeyer-Choquet operators

2017 ◽  
Vol 33 (1) ◽  
pp. 49-58
Author(s):  
SORIN G. GAL ◽  
◽  
SORIN TRIFA ◽  
Keyword(s):  
Modulus Of Continuity ◽  
Pointwise Approximation ◽  
Dimensional Simplex ◽  
Set Functions ◽  
Quantitative Estimates ◽  
Durrmeyer Operator ◽  
Choquet Integrals

For the qualitative results of uniform and pointwise approximation obtained in [8], we present here general quantitative estimates in terms of the modulus of continuity and of a K-functional, in approximation by the generalized multivariate Bernstein-Durrmeyer operator Mn,Γn,x, written in terms of Choquet integrals with respect to a family of monotone and submodular set functions, Γn,x, on the standard d-dimensional simplex. If d = 1 and the Choquet integrals are taken with respect to some concrete possibility measures, the estimate in terms of the modulus of continuity is detailed. Examples improving the estimates given by the classical operators also are presented.

On the generalized k-order additivity for absolutely monotone set functions

2018 ◽  
Vol 23 (15) ◽  
pp. 6043-6050 ◽  
Author(s):  
Biljana Mihailović ◽  
Martin Kalina ◽  
Mirjana Štrboja
Keyword(s):  
Set Functions ◽  
Absolutely Monotone

Sugeno integral based on absolutely monotone real set functions

2010 ◽  
Vol 161 (22) ◽  
pp. 2857-2869 ◽  
Author(s):  
Biljana Mihailović ◽  
Endre Pap
Keyword(s):  
Sugeno Integral ◽  
Set Functions ◽  
Absolutely Monotone

Quantitative approximation by Stancu-Durrmeyer-Choquet-Šipoš operators

2019 ◽  
Vol 69 (3) ◽  
pp. 625-638
Author(s):  
Sorin G. Gal
Keyword(s):  
Modulus Of Continuity ◽  
Dimensional Simplex ◽  
Set Functions ◽  
Quantitative Estimates ◽  
Choquet Integrals

Abstract In this paper we present general quantitative estimates in terms of the modulus of continuity and of a K-functional, in approximation by the generalized multivariate Stancu-Durrmeyer-Choquet-Šipoš operators $\begin{array}{} M_{n, \Gamma_{n, x}}^{(\beta, \gamma)} \end{array} $, with 0 ≤ β ≤ γ, written in terms of Choquet and Šipoš integrals with respect to a family of monotone and submodular set functions, Γn, x, on the standard d-dimensional simplex. If d = 1 and the Choquet integrals are taken with respect to some concrete possibility measures, the estimate in terms of the modulus of continuity is detailed. Examples improving the estimates given by the classical operators also are presented.

The implementation of set functions in APL

1998 ◽  
Vol 28 (3) ◽  
pp. 31-32
Author(s):  
Joseph De Kerf
Keyword(s):  
Set Functions

On a Choquet-Stieltjes type integral on intervals

2019 ◽  
Vol 69 (4) ◽  
pp. 801-814 ◽  
Author(s):  
Sorin G. Gal
Keyword(s):  
Lebesgue Measure ◽  
Choquet Integral ◽  
Stieltjes Integral ◽  
Line Integral ◽  
Type Integral ◽  
Choquet Integrals ◽  
Lebesgue Measures ◽  
Stieltjes Type

Abstract In this paper we introduce a new concept of Choquet-Stieltjes integral of f with respect to g on intervals, as a limit of Choquet integrals with respect to a capacity μ. For g(t) = t, one reduces to the usual Choquet integral and unlike the old known concept of Choquet-Stieltjes integral, for μ the Lebesgue measure, one reduces to the usual Riemann-Stieltjes integral. In the case of distorted Lebesgue measures, several properties of this new integral are obtained. As an application, the concept of Choquet line integral of second kind is introduced and some of its properties are obtained.

Fuzzy Measures and Choquet Integrals based on Fuzzy Covering Rough Sets

2021 ◽  
pp. 1-1
Author(s):  
Xiaohong Zhang ◽  
Jingqian Wang ◽  
Jianming Zhan ◽  
Jianhua Dai
Keyword(s):  
Rough Sets ◽  
Fuzzy Measures ◽  
Choquet Integrals
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