dc.contributor.author
Song, Yutong
dc.contributor.author
Deng, Yong
dc.date.accessioned
2021-08-30T09:58:22Z
dc.date.available
2021-08-27T02:49:46Z
dc.date.available
2021-08-30T09:48:09Z
dc.date.available
2021-08-30T09:58:22Z
dc.date.issued
2021-08
dc.identifier.issn
1841-9836
dc.identifier.issn
1841-9844
dc.identifier.other
10.15837/ijccc.2021.4.4413
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/502409
dc.identifier.doi
10.3929/ethz-b-000502409
dc.description.abstract
A power set of a set S is defined as the set of all subsets of S, including set S itself and empty set, denoted as P(S) or 2(S). Given a finite set S with vertical bar S vertical bar= n hypothesis, one property of power set is that the amount of subsets of S is vertical bar P(S)vertical bar= 2n. However, the physica meaning of power set needs exploration. To address this issue, a possible explanation of power set is proposed in this paper. A power set of n events can be seen as all possible k-combination, where k ranges from 0 to n. It means the power set extends the event space in probability theory into all possible combination of the single basic event. From the view of power set, all subsets or all combination of basic events, are created equal. These subsets are assigned with the mass function, whose uncertainty can be measured by Deng entropy. The relationship between combinatorial number, Pascal's triangle and power set is revealed by Deng entropy quantitively from the view of information measure.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Agora University
en_US
dc.rights.uri
dc.subject
Power set
en_US
dc.subject
Combinatorial number
en_US
dc.subject
Pascal's triangle
en_US
dc.subject
Dempster-Shafer evidence theory
en_US
dc.subject
mass function
en_US
dc.subject
Shannon entropy
en_US
dc.subject
Deng entropy
en_US
dc.title
Entropic Explanation of Power Set
en_US
dc.type
Journal Article
Creative Commons Attribution-NonCommercial 4.0 International
ethz.journal.title
International Journal of Computers, Communications & Control
ethz.journal.volume
16
en_US
ethz.journal.issue
4
en_US
ethz.pages.start
4413
en_US
ethz.size
8 p.
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.identifier.wos
ethz.publication.place
en_US
ethz.publication.status
published
en_US
ethz.date.deposited
2021-08-27T02:50:09Z
ethz.source
WOS
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2021-08-30T09:48:16Z
ethz.rosetta.lastUpdated
2022-03-29T11:22:06Z
ethz.rosetta.versionExported
true
ethz.COinS
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