|
|
Morphisms of Dempster's Semigroup: A Revision and Interpretation
Daniel, Milan
Analyzing three new approaches to interpretation, definition, and measurement of conflicts of belief Functions (BFs), we previously observed a possibility of expression of a BF Bel as Dempster's sum of non-conflicting BF Bel0 with the same plausibility decisional support as the original BF Bel has and of indecisive BF BelS which does not prefer any of the elements of frame of discernment. Based on this observation, the theory of homomorphisms of Dempster's semigroup (the algebra of non-extremal BFs on 2-element frame of discernment with Dempster's rule as its binary operation) is updated in the present contribution. New homomorphisms are introduced; their interpretation and relation to the original ones are presented.
|
|
| |
|
|
New Approach to Conflicts within and between Belief Functions
Daniel, Milan
This study deals with conflicts of belief functions. Internal conflicts of belief functions and conflicts between belief functions are described and analyzed here. Differences of belief functions are distinguished from conflicts between them. Three new different approaches to conflicts are presented: combinational, plausibility and comparative. The presented approaches to conflicts are compared to Liu's interpretation of conflicts.
Fulltext: content.csg -  PDF
Plný tet: v1062-09 - PDF
|
|
|
Podmiňování domnění v DSmT
Daniel, Milan
Basic notions from both Dempster-Shafer theory and DSmT (Dezert-Smarandache theory) are briefly reminded, followed by a recapitulation of the existing results on DSm conditioning. Analogically to the analysis of belief conditioning in the classical case, the existing DSm belief conditioning rules (BCRs) are analysed and the new generalized plain BCR is defined, a general formula for DSm BCRs is presented, and the general DSm BCR is defined. Further, the negative conditioning in the lattice based DSm approach is introduced, the negative plain and negative Dempster's BCRs are defined and first results of these new rules are presented. Finally a wide area of open problems of negative DSm belief conditioning and its relation to positive conditioning is sketched.
|
|
|
Podmiňovací pravidla pro klasické domněnkové funkce
Daniel, Milan
The classic belief conditioning rules (BCRs) and DSm BCRs applied to classic belief functions are briefly recalled in the contribution. A general idea of belief conditioning by a given evidence is analysed and a new plain BCR is presented. This rule is compared with both the classic and the DSm BCRs. Finally, general formulas for described BCRs and a new general BCR are presented and defined.
|
|
| |
|
|
Kompozicionální modely domněnkvých funkcí
Jiroušek, Radim ; Vejnarová, Jiřina ; Daniel, Milan
After it has been successfully done in probability and possibility theories, the paper is the first attempt to introduce the operator of composition also for belief functions. We prove that the proposed definition preserves all the necessary properties of the operator enabling us to define compositional models as an efficient tool for multidimensional models representation.
|
|
|
Několik poznámek a otázek k Josangově uhlazenému zhrubění.
Daniel, Milan
Definitions of two different ways of coarsening of basic belief assignments to opinions - simple coarsening and smooth coarsening – are recalled in this contribution. A relation of results of combination of smooth opinions using the consensus operator to belief functions on an original $n$-element frame of discernment is examined. A question of an interpretation of smoothly coarsened opinions is discussed.
|
|
| |
|
|
Co je to Hybridní DSm Pravidlo pro kombinování domněnkových funkcí?
Daniel, Milan
This contribution is dealing with DSm theory of belief functions. Two different versions of hybrid DSm combination rule are presented. Inconsistencies of the newer version are observed and its corrections are suggested. New DSmH rules, which produce more specified results are suggested, and a schema, which covers a large family of combination rules derived from the generalized conjunctive combination rule, is presented.
|
guest ::
RSS feed.