Fabio Cuzzolin's Belief Functions: Theory and Applications: Third PDF

By Fabio Cuzzolin

This e-book constitutes the completely refereed complaints of the 3rd overseas convention on trust features, trust 2014, held in Oxford, united kingdom, in September 2014. The forty seven revised complete papers awarded during this publication have been rigorously chosen and reviewed from fifty six submissions. The papers are prepared in topical sections on trust blend; desktop studying; functions; thought; networks; info fusion; info organization; and geometry.

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

Example text

Certainly, the formula μ= m(B)η B , B∈2X is also valid, but values of m is not non-negative for the general case. The model of uncertainty based on monotone measures uses set functions that can be interpreted as lower or upper estimates of probabilities. A monotone measure μ is called an lower probability if there is a P ∈ Mpr with μ P . For the sake of convenience, we will use the following notations: Mmon is the set of all monotone measures on 2X ; Mlow is the set of all monotone measures on 2X .

213-241. Brussels, ECSC, EEC, EAFC (1992) 9. : Aggregation Functions. Cambridge University Press (2009) 10. : Combining sources of evidence with reliability and importance for decision making. Central European Journal of Operations Research, 1–20 (December 2013) 11. : Axiomatic approaches to formulas for combining likelihoods or evidence. Journal of Statistical Computation and Simulation 31(1), 49–54 (1989) 12. : About Relation between the Measure of Conflict and Decreasing of Ignorance in Theory of Evidence.

Let g be a belief function that can be represented by g = B∈2X \{∅} mg (B)η B ∈ Bel(X). Then the generalized Hartley’s measure is defined by [6] GH (g) = B∈2X \{∅} mg (B)log2 |B|. Definition 1. [3]. A functional f : Bel(X) → [0, 1] is called an imprecision index if the following conditions are fulfilled: 1. if g is a probability measure then f (g) = 0; 2. e. g1 (A) ≤ g2 (A) for all A ∈ 2X ); 3. f η X = 1. We call the imprecision index strict if f (g) = 0 ⇔ g is a probability measure. , k, we have k j=1 αj gj = 35 αj f (gj ).

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