Conditioning w.r.t. random sets. Part 2: combination rules.
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| Title: | Conditioning w.r.t. random sets. Part 2: combination rules. |
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| Authors: | Bronevich, Andrey G.1 (AUTHOR) brone@mail.ru |
| Source: | International Journal of General Systems. Aug2025, Vol. 54 Issue 6, p787-824. 38p. |
| Subjects: | Random sets, Dempster-Shafer theory, Consensus (Social sciences), Uncertainty (Information theory) |
| Abstract: | Part 2 of this article is devoted to the analysis of a new class of combination rules on belief functions generated by conditioning w.r.t. random sets and their linear convex combinations. Each such rule obeys two requirements: the consensus requirement with the conjunction rule means that this rule coincides with Dempster's rule on non-conflicting sources of information, and the consensus requirement with a mixture rule means that the result must be a specialization of their mixture combination. We show that this new class of combination rules is closed under convex combinations of such rules and their compositions. This allows us to implement the conflict management using the introduced functionals for measuring the specialization relation on belief functions. We also introduce similar rules for idempotent combination rules on credal sets obeying the similar consensus requirements and study the results obtained using various examples. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | Part 2 of this article is devoted to the analysis of a new class of combination rules on belief functions generated by conditioning w.r.t. random sets and their linear convex combinations. Each such rule obeys two requirements: the consensus requirement with the conjunction rule means that this rule coincides with Dempster's rule on non-conflicting sources of information, and the consensus requirement with a mixture rule means that the result must be a specialization of their mixture combination. We show that this new class of combination rules is closed under convex combinations of such rules and their compositions. This allows us to implement the conflict management using the introduced functionals for measuring the specialization relation on belief functions. We also introduce similar rules for idempotent combination rules on credal sets obeying the similar consensus requirements and study the results obtained using various examples. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 03081079 |
| DOI: | 10.1080/03081079.2024.2427246 |
