View in EDS HTML Full Text PDF Full Text

Conditioning w.r.t. random sets. Part 1: basic notions and results.

Saved in:
Bibliographic Details
Title: Conditioning w.r.t. random sets. Part 1: basic notions and results.
Authors: Bronevich, Andrey G.1 (AUTHOR) brone@mail.ru
Source: International Journal of General Systems. Aug2025, Vol. 54 Issue 6, p745-786. 42p.
Subjects: Dempster-Shafer theory, Random sets, Uncertainty (Information theory), Set-valued maps, Probability theory
Abstract: The most controversial and basic construction in Dempster–Shafer theory is Dempster's combination rule. We analyze this concept through the conditioning with respect to a random set introduced in the paper. The paper has two parts. In Part 1, we describe the basic constructions in Dempster–Shafer theory considering multivalued mappings (random sets), the axiomatic approach proposed by G. Shafer, and the transferable belief model (TBM). We also introduce generalized credal sets as an extension of TBM and the theory of imprecise probabilities. After that, we introduce the conditioning w.r.t. a random set with various kinds of prior information and successive conditioning, and analyze, when this conditioning coincides with Dempster's rule. We show that the successive conditioning can be described by the intersection of generalized credal sets in the case of vacuous prior information and unknown interaction among random sets. Part 2 is devoted to the description of a new class of combination rules constructed by conditioning w.r.t. random sets, and by linear combinations of such rules. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of General Systems is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
Full text is not displayed to guests.
FullText Links:
  – Type: pdflink
Text:
  Availability: 1
Header DbId: egs
DbLabel: Engineering Source
An: 186874821
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Conditioning w.r.t. random sets. Part 1: basic notions and results.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Bronevich%2C+Andrey+G%2E%22">Bronevich, Andrey G.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> brone@mail.ru</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+General+Systems%22">International Journal of General Systems</searchLink>. Aug2025, Vol. 54 Issue 6, p745-786. 42p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Dempster-Shafer+theory%22">Dempster-Shafer theory</searchLink><br /><searchLink fieldCode="DE" term="%22Random+sets%22">Random sets</searchLink><br /><searchLink fieldCode="DE" term="%22Uncertainty+%28Information+theory%29%22">Uncertainty (Information theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Set-valued+maps%22">Set-valued maps</searchLink><br /><searchLink fieldCode="DE" term="%22Probability+theory%22">Probability theory</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: The most controversial and basic construction in Dempster–Shafer theory is Dempster's combination rule. We analyze this concept through the conditioning with respect to a random set introduced in the paper. The paper has two parts. In Part 1, we describe the basic constructions in Dempster–Shafer theory considering multivalued mappings (random sets), the axiomatic approach proposed by G. Shafer, and the transferable belief model (TBM). We also introduce generalized credal sets as an extension of TBM and the theory of imprecise probabilities. After that, we introduce the conditioning w.r.t. a random set with various kinds of prior information and successive conditioning, and analyze, when this conditioning coincides with Dempster's rule. We show that the successive conditioning can be described by the intersection of generalized credal sets in the case of vacuous prior information and unknown interaction among random sets. Part 2 is devoted to the description of a new class of combination rules constructed by conditioning w.r.t. random sets, and by linear combinations of such rules. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of General Systems is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=186874821
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1080/03081079.2024.2427245
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 42
        StartPage: 745
    Subjects:
      – SubjectFull: Dempster-Shafer theory
        Type: general
      – SubjectFull: Random sets
        Type: general
      – SubjectFull: Uncertainty (Information theory)
        Type: general
      – SubjectFull: Set-valued maps
        Type: general
      – SubjectFull: Probability theory
        Type: general
    Titles:
      – TitleFull: Conditioning w.r.t. random sets. Part 1: basic notions and results.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Bronevich, Andrey G.
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 08
              Text: Aug2025
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-print
              Value: 03081079
          Numbering:
            – Type: volume
              Value: 54
            – Type: issue
              Value: 6
          Titles:
            – TitleFull: International Journal of General Systems
              Type: main
ResultId 1