By Ronald R. Yager, Liping Liu

This booklet brings jointly a set of vintage study papers at the Dempster-Shafer thought of trust services. via bridging fuzzy common sense and probabilistic reasoning, the speculation of trust capabilities has develop into a chief device for wisdom illustration and uncertainty reasoning in specialist platforms. This ebook will function the authoritative reference within the box of evidential reasoning and an immense archival reference in quite a lot of parts together with uncertainty reasoning in man made intelligence and choice making in economics, engineering, and administration. From over a hundred and twenty nominated contributions, the editors chosen 30 papers, that are broadly considered as classics and should proceed to make affects at the destiny improvement of the sphere. The contributions are grouped into seven sections, together with conceptual foundations, theoretical views, theoretical extensions, replacement interpretations, and functions to man made intelligence, decision-making, and statistical inferences. The ebook additionally contains a foreword via Dempster and Shafer reflecting the improvement of the idea within the final 40 years, and an advent describing the fundamental components of the speculation and the way each one paper contributes to the sphere.

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**Extra resources for Classic Works of the Dempster-Shafer Theory of Belief Functions**

**Example text**

There are many connections between fuzzy logic and belief functions. As we have seen earlier, possibility and necessity functions are consonant plausibility and support functions that have nested focal elements. Chapter 14, by 30 L. Liu and R. R. Yager Dubois and Prade, exposed another connection between bodies of evidence and fuzzy sets. , A = {x, y, z}. The concept of a fuzzy set extends it to include a membership function m → [0, 1] describing a graded assessment of the membership of elements in relation to a set.

It illustrated that both Bayesian theory and the theory of belief functions were formal languages for 1 Classic Works of the Dempster-Shafer Theory of Belief Functions 21 one to analyze evidence and express his degrees of belief; they had the usual components of a language, including vocabularies, semantics, and syntax. It suggested that making a probability judgment was a process of conducting a mental experiment and hence the quality of the experimental design aﬀected the quality of the judgment.

Besides x and θ, the ﬁducial method introduces a so-called pivotal variable u, which is assumed to follow the uniform distribution U (0, 1), so that u = F (x, θ). (16) Suppose, for each value x, F (x, θ) is monotonic in θ. Equation 16 will admit a unique solution θ = θ(u, x) (17) for each u ∈ (0, 1). Assuming no prior probabilities, Fisher deﬁned the ﬁducial distribution of θ, given the observed value x, as the distribution of θ implied by (17) when x is regarded as ﬁxed and u is uniformly distributed.