By Fabio Cuzzolin

This ebook constitutes the completely refereed court cases of the 3rd overseas convention on trust services, trust 2014, held in Oxford, united kingdom, in September 2014. The forty seven revised complete papers offered during this e-book have been rigorously chosen and reviewed from fifty six submissions. The papers are equipped in topical sections on trust mix; computing device studying; functions; concept; networks; details fusion; information organization; and geometry.

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Extra info for Belief Functions: Theory and Applications: Third International Conference, BELIEF 2014, Oxford, UK, September 26-28, 2014. Proceedings

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MDP (A) = (6) A1 ∪A2 =A Any combining rule of two bodies of evidence induces aggregation of two belief functions which correspond to these bodies. 32 4 A. Lepskiy Combining Rule Both the Aggregation of Evidence We will consider an operator ϕ : Bel2 (X) → Bel(X) that is called the aggregation of two belief functions g1 , g2 ∈ Bel(X) in one belief function g = ϕ(g1 , g2 ) ∈ Bel(X). The vector of bpa (mg (B))B⊆X corresponds bijective (with the help of M¨ obius transform) to belief function g ∈ Bel(X) if we define some ordering of all subsets of the universal set X: g ↔ mg = (mg (B))B⊆X .

For tx ,¬tp x instance, consider state h{x and testimony x ∈ {x1 , x3 }, then one should 3 ,x4 } deduce {x1 , x3 } {x3 , x4 } = {x3 }. , the source is a negative liar for all x ∈ A and truthful for all x ∈ A, in which case x ∈ X is a possible value for x iff x ∈ B or x ∈ A, and thus one should conclude that x ∈ B ∪ A. More generally, as can be seen from Table 1, the couples (t1 , t2 ) ∈ Tx2 yields all possible binary Boolean connectives. t ,¬tp ¬tn ,t Of particular interest in this paper are the states hAx x and hA x x , which have already been discussed, and the states htAx ,¬tx (the source is truthful for all x ,tx x ∈ A and non truthful for all x ∈ A) and h¬t (the source is non truthful A for all x ∈ A and truthful for all x ∈ A), which yield respectively x ∈ B∩A and x ∈ B∪A.

4 Generalized Dempster-Shafer Rules and the Partial Order of Specialization Given a belief function Bel1 and m1 is its bba. In the next we will consider set Φ(A, B) = 1 functions Φ : 2X × 2X → [0, 1] with the following property: B∈2X for any B ∈ 2 . Then a belief function Bel2 with the bba m2 (B) = X A∈2X Φ(A, B)m1 (A) is the linear transform of Bel1 produced by the linear operator Φ. One can distinguish contraction and expansive linear transforms. A linear transform Φ is called the contraction transform if Φ(A, B) = 0 for A ⊃ B, and it is called expansive if Φ(A, B) = 0 for A ⊂ B.

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