By John Grant, Francesco Parisi (auth.), Zongmin Ma, Li Yan (eds.)

This e-book covers a fast-growing subject in nice intensity and specializes in the applied sciences and purposes of probabilistic info administration. It goals to supply a unmarried account of present experiences in probabilistic information administration. the target of the e-book is to supply the cutting-edge info to researchers, practitioners, and graduate scholars of knowledge expertise of clever info processing, and even as serving the data expertise expert confronted with non-traditional purposes that make the applying of traditional methods tough or impossible.

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Here o1, o2, …, ok have the same object identifier. Let the probability measure of object oi (1 ≤ i ≤ k) be oi (pe). Then we have i = 1, 2, …, k oi (pe) ≤ 1. The probability measure associated with an object is a crisp one expressed by a precise value when it is definitely known. Also it is possible that the probability measure associated with an object is fuzzily known. At this point, the probability measure associated with the object is a fuzzy probability measure and is expressed by a possibility distribution.

In other words, o1 and o2 are two equivalent objects with degree of o (fpM). 5)}. 5)}. For two probabilistic objects with fuzzy measures, they may be semantically similar even if they are not equivalent. Here we introduce a notation of semantic similarity between two probabilistic objects with fuzzy measures. For two probabilistic classes with fuzzy measures, say c1 and c2, let c1 contain attributes {a1, a2, …, ak, fpM1} and c2 contain attributes {b1, b2, …, bl, fpM2}, in which fpM1 and fpM2 are the fuzzy probabilistic attributes of c1 and c2, respectively.

A membership function μF: U → [0, 1] is defined for F, where μF (u) for each u ∈ U denotes the membership degree of u in the fuzzy set F. , (un, μF (un))} In fuzzy set F, each element may or may not belong to F and has a membership degree to F that needs to be explicitly indicated. So an element in F (say ui) is associated with its membership degree (say μF (ui)) and these occur together in the form of μF (ui)/ui. When the membership degrees indicate that all elements in F belong to F with membership degrees of exactly 1, fuzzy set F reduces to the conventional set.

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