On topological properties of the Choquet weak convergence of capacity functionals of random sets
In view of the recent interests in random sets in information technology, such as models for imprecise data in intelligent systems, morphological analysis in image processing, we present, in this paper, some contributions to the foundation of random set theory, namely, a complete study of topologica...
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th-cmuir.6653943832-609882018-09-10T04:06:52Z On topological properties of the Choquet weak convergence of capacity functionals of random sets S. Dhompongsa A. Kaewkhao S. Saejung Computer Science Decision Sciences Engineering Mathematics In view of the recent interests in random sets in information technology, such as models for imprecise data in intelligent systems, morphological analysis in image processing, we present, in this paper, some contributions to the foundation of random set theory, namely, a complete study of topological properties of capacity functionals of random sets, generalizing weak convergence of probability measures. These results are useful for investigating the concept of Choquet weak convergence of capacity functionals leading to tractable criteria for convergence in distribution of random sets. The weak topology is defined on the space of all capacity functionals on Rd. We show that this topological space is separable and metrizable. © 2006 Elsevier Inc. All rights reserved. 2018-09-10T04:02:28Z 2018-09-10T04:02:28Z 2007-04-15 Journal 00200255 2-s2.0-33846624765 10.1016/j.ins.2006.11.004 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=33846624765&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/60988 |
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Computer Science Decision Sciences Engineering Mathematics |
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Computer Science Decision Sciences Engineering Mathematics S. Dhompongsa A. Kaewkhao S. Saejung On topological properties of the Choquet weak convergence of capacity functionals of random sets |
| description |
In view of the recent interests in random sets in information technology, such as models for imprecise data in intelligent systems, morphological analysis in image processing, we present, in this paper, some contributions to the foundation of random set theory, namely, a complete study of topological properties of capacity functionals of random sets, generalizing weak convergence of probability measures. These results are useful for investigating the concept of Choquet weak convergence of capacity functionals leading to tractable criteria for convergence in distribution of random sets. The weak topology is defined on the space of all capacity functionals on Rd. We show that this topological space is separable and metrizable. © 2006 Elsevier Inc. All rights reserved. |
| format |
Journal |
| author |
S. Dhompongsa A. Kaewkhao S. Saejung |
| author_facet |
S. Dhompongsa A. Kaewkhao S. Saejung |
| author_sort |
S. Dhompongsa |
| title |
On topological properties of the Choquet weak convergence of capacity functionals of random sets |
| title_short |
On topological properties of the Choquet weak convergence of capacity functionals of random sets |
| title_full |
On topological properties of the Choquet weak convergence of capacity functionals of random sets |
| title_fullStr |
On topological properties of the Choquet weak convergence of capacity functionals of random sets |
| title_full_unstemmed |
On topological properties of the Choquet weak convergence of capacity functionals of random sets |
| title_sort |
on topological properties of the choquet weak convergence of capacity functionals of random sets |
| publishDate |
2018 |
| url |
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=33846624765&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/60988 |
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