Conditioning w.r.t. random sets. Part 1: basic notions and results.
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| Title: | Conditioning w.r.t. random sets. Part 1: basic notions and results. |
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| 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] |
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| Database: | Engineering Source |
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| 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] |
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| ISSN: | 03081079 |
| DOI: | 10.1080/03081079.2024.2427245 |
