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Two Composition Operators for Belief Functions Revisited
Jiroušek, Radim ; Kratochvíl, Václav ; Shenoy, P. P.
In probability theory, compositional models are as powerful as Bayesian networks. However, the relation between belief-function graphical models and the corresponding compositional models is much more complicated due to several reasons. One of them is that there are two composition operators for belief functions. This paper deals with their main properties and presents sufficient conditions under which they yield the same results.
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A Step towards Upper-bound of Conflict of Belief Functions based on Non-conflicting Parts
Daniel, M. ; Kratochvíl, Václav
This study compares the size of conflict based on non-conflicting parts of belief functions $Conf$ with the sum of all multiples of bbms of disjoint focal elements of belief functions in question. In general, we make an effort to reach a simple upper bound function for $Conf$. (Nevertheless, the maximal value of conflict is, of course, equal to 1 for fully conflicting belief functions). We apply both theoretical research using the recent results on belief functions and also experimental computational approach here.
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Hidden Auto-Conflict in the Theory of Belief Functions
Daniel, M. ; Kratochvíl, Václav
Hidden conflicts of belief functions in some cases where the sum of all multiples of conflicting belief masses being equal to zero were observed. Relationships of hidden conflicts and auto-conflicts of belief functions are pointed out. We are focused on hidden auto-conflicts here - on hidden conflicts appearing when three or more numerically same belief functions are combined. Hidden auto-conflict is a kind of internal conflict. Degrees of hidden auto-conflicts and full non-conflictness are defined and analysed. Finally, computational issues of hidden auto-conflicts and non-conflictness are presented.
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Homomorphic Coordinates of Dempster’s Semigroup
Daniel, Milan
Coordinates of belief functions on two-element frame of discernment are defined using homomorphisms of Dempster’s semigroup (the algebra of belief functions with Dempster’s rule). Three systems of the coordinates (h-f, h-f0, and coordinates based on decomposition of belief functions) are analysed with a focus to their homomorphic properties. Further, ideas of generalisation of the investigated systems of coordinates to general finite frame of discernment are presented.
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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
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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.
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