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.6653943832-52742014-08-30T02:56:20Z On topological properties of the Choquet weak convergence of capacity functionals of random sets Dhompongsa S. Kaewkhao A. Saejung S. 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. 2014-08-30T02:56:20Z 2014-08-30T02:56:20Z 2007 Article 00200255 10.1016/j.ins.2006.11.004 ISIJB http://www.scopus.com/inward/record.url?eid=2-s2.0-33846624765&partnerID=40&md5=133482cc609f19de5ac1a3aabc499900 http://cmuir.cmu.ac.th/handle/6653943832/5274 English |
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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 |
Article |
| author |
Dhompongsa S. Kaewkhao A. Saejung S. |
| spellingShingle |
Dhompongsa S. Kaewkhao A. Saejung S. On topological properties of the Choquet weak convergence of capacity functionals of random sets |
| author_facet |
Dhompongsa S. Kaewkhao A. Saejung S. |
| author_sort |
Dhompongsa S. |
| 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 |
2014 |
| url |
http://www.scopus.com/inward/record.url?eid=2-s2.0-33846624765&partnerID=40&md5=133482cc609f19de5ac1a3aabc499900 http://cmuir.cmu.ac.th/handle/6653943832/5274 |
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1681420394223894528 |