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# Conflict between Belief Functions: A New Measure Based on Their Non-conflicting Parts

1. 1.
0434587 - ÚI 2015 RIV CH eng C - Konferenční příspěvek (zahraniční konf.)
Daniel, Milan
Conflict between Belief Functions: A New Measure Based on Their Non-conflicting Parts.
Belief Functions: Theory and Applications. Cham: Springer, 2014 - (Cuzzolin, F.), s. 321-330. Lecture Notes in Artificial Intelligence, 8764. ISBN 978-3-319-11190-2. ISSN 0302-9743.
[BELIEF 2014. International Conference /3./. Oxford (GB), 26.09.2014-28.09.2014]
Grant CEP: GA ČR GAP202/10/1826
Institucionální podpora: RVO:67985807
Klíčová slova: belief functions * Dempster-Shafer theory * uncertainty * Dempster’s semigroup * internal conflict * conflict between belief functions * non-conflicting part of belief function * conflicting part of belief function
Kód oboru RIV: BA - Obecná matematika

When combining belief functions by conjunctive rules of combination, conflicts often appear, which are assigned to empty set by the non-normalised conjunctive rule or normalised by Dempster’s rule of combination in Dempster-Shafer theory. Combination of conflicting belief functions and interpretation of their conflicts is often questionable in real applications; hence a series of alternative combination rules were suggested and a series of papers on conflicting belief functions have been published and conflicts of belief functions started to be investigated. This theoretical contribution introduces a new definition of conflict between two belief functions on a general finite frame of discernment. Its idea is based on H´ajek-Vald´es algebraic analysis of belief functions, on our previous study of conflicts of belief functions, where internal conflicts of belief functions are distinguished from a conflict between belief functions, and on the decomposition of a belief function into its conflicting and non-conflicting parts. Basic properties of this newly defined conflict are presented, analyzed and briefly compared with our previous approaches to conflict as well as with Liu’s degree of conflict.