By Bernadette Bouchon-Meunier, Giulianella Coletti, Ronald R. Yager

The amount ''Modern info Processing: From idea to Applications,'' edited by means of Bernadette Bouchon-Meunier, Giulianella Coletti and Ronald Yager, is a set of rigorously chosen papers drawn from this system of IPMU'04, which was once held in Perugia, Italy.

The e-book represents the cultural coverage of IPMU convention which isn't excited about slender variety of methodologies, yet to the contrary welcomes the entire theories for the administration of uncertainty and aggregation of data in clever platforms, supplying a medium for the alternate of principles among theoreticians and practitioners in those and comparable parts.

The publication consists through 7 sections:

UNCERTAINTY

PREFERENCES

CLASSIFICATION and information MINING

AGGREGATION AND MULTI-CRITERIA choice MAKING

KNOWLEDGE REPRESENTATION

.The ebook contributes to enhancement of our skill to deal successfully with uncertainty in all of its manifestations.

.The publication will help to construct brigs between theories and strategies tools for the administration of uncertainty.

.The publication addresses matters that have a place of centrality in our information-centric global.

.The booklet provides attention-grabbing effects dedicated to representing wisdom: the objective is to catch the subtlety of human wisdom (richness) and to permit laptop manipulation (formalization).

.The e-book contributes to the target: an effective use of the data for a superb choice strategy.

APPLIED domain names

· The booklet contributes to enhancement of our skill to deal successfully with uncertainty in all of its manifestations.

· The booklet might help to construct brigs between theories and techniques tools for the administration of uncertainty.

· The publication addresses concerns that have a place of centrality in our information-centric world.

· The ebook provides attention-grabbing effects dedicated to representing wisdom: the target is to trap the subtlety of human wisdom (richness) and to permit computing device manipulation (formalization).

· The publication contributes to the target: an effective use of the knowledge for a very good determination process

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**Extra resources for Modern Information Processing. From Theory to Applications**

**Example text**

2] deals only with classical D-S approach with (normalized) Dempster's rule of combination, it compares pignistic and plausibility probabilistic transformations. While [1] considers a more general field of imprecise probabilities. This contribution summarizes and compares the relevant results from [1], [2] and [7] together with new results on the topic. Two approaches to consistency of probabilistic transformations ulb-consistency and combination consistency are introduced in Section 3. Various probabilistic transformations from [1,2,7] are presented in the first half of fourth section.

Related algebraic Notions Let us recall the following from algebraic analyses of belief functions on 2-element frame of discernment, see e. g. [5,6,12,13]. Every 2D BF bel uniquely corresponds to the pair (m(a;i), m{u2)) due to 2D^(^) = 1 — ( 2 D ^ ( ^ I ) H-2D ^ ( ^ 2 ) ) . The set of all 2D BFs is denoted as DQ, the set of all Bayesian 2D BFs, i. e. m(a;i) -h m(a;2) = 1 is denoted as G, the set of 2D BFs such that m(a;i) = m(a;2) is denoted as S and the set where m(a;2) = 0 as 5i, analogically m(a;i) = 0 in 52- For the special belief functions 0 and 0' it holds that 2D0 = (0?

Proof: One has the following situations: a. Suppose that 7r(A|B) = 7r(A'^|B) = 1, so Uo{A AB)= min{l, Ilo{B)} HoiA A B) = min{Tr{B\A),Uo{A)} UoiA A B") = min{l, Uo{B'')} Uo{A A B") = mm{Tr{B'=\A), Uo{A)} So UoiA" AB)= min{l, Uo{B)} UoiA'' A B) = mm{TT{B\A''),Uo{A'')} Ilo{A'= A B'') = min{l, UoiB")} UoiA" A B") = miniTriB"]A"), UoiA")} If 7r(5|A'=) = 7r(B^|A<=) = 1, then HoiA* A B*) = 1 and the condition (4) holds. If 7r(B|A'=) < 1, then UoiA" A B'=) = 1 = Ilo{A A B<=), while UoiA" A B) = UiBlA") = UoiB) = Tr{B\A) = RoiA A B) < 1.