Vector-Valued Choquet Integrals for Set Functions and Bi-capacities

2012 ◽  
pp. 218-227
Author(s):  
Eiichiro Takahagi
Keyword(s):  
Set Functions ◽  
Choquet Integrals ◽  
Vector Valued

scholarly journals On the Differentiability of Vector Valued Additive Set Functions

2013 ◽  
Vol 03 (08) ◽  
pp. 653-659 ◽  
Author(s):  
Mangatiana A. Robdera ◽  
Dintle Kagiso
Keyword(s):  
Set Functions ◽  
Vector Valued

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.

scholarly journals Martingales of vector valued set functions

1969 ◽  
Vol 30 (2) ◽  
pp. 533-548 ◽  
Author(s):  
John Uhl
Keyword(s):  
Set Functions ◽  
Vector Valued
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