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Dempster shafer theory,23

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3.3 Dempster-Shafer Theory ➢ Dempster-Shafer theory is an approach to combining evidence ➢ Dempster (1967) developed means for combining degrees of belief derived from independent items of evidence. ➢ His student, Glenn Shafer (1976), developed method for obtaining degrees of belief for one question from subjective probabilities for a related question ➢ People working in Expert Systems in the 1980s saw their approach as ideally suitable for such systems. ➢ Each fact has a degree of support, between 0 and 1: ✓ 0 No support for the fact ✓ 1 full support for the fact ➢ Differs from Bayesian approah in that: ✓ Belief in a fact and its negation need not sum to 1. ✓ Both values can be 0 (meaning no evidence for or against the fact) Set of possible conclusions: Θ Θ = { θ1 , θ2 , …, θn } Where: ✓ Θ is the set of possible conclusions to be drawn ✓ Each θi is mutually exclusive: at most one has to be true. ✓ Θ is Exhaustive: At least one θi has to be true. Frame of discernment Θ = { θ1 , θ2 , …, θn } ➢ Bayes was concerned with evidence that supported single conclusions (e.g., evidence for each outcome θi in Θ): ➢ p(θi| E) ➢ D-S Theoryis concerned with evidences which support ➢ subsets of outcomes in Θ, e.g., θ1 v θ2 v θ3 or {θ1, θ2, θ3} ➢ The “frame of discernment” (or “Power set”) of Θ is the set of all possible subsets of Θ: E.g., if Θ = {θ1, θ2, θ3} ➢ Then the frame of discernment of Θ is: ( Ø, θ ...
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