Non-conflicting and Conflicting Parts of Belief Functions

Non-conflicting and conflicting parts of belief functions are introduced in this study. The unique decomposition of a belief function defined on a two-element frame of discernment to non-conflicting and indecisive conflicting belief function is presented. Several basic statements about algebra of belief functions on a general finite frame of discernment are introduced and unique non-conflicting part of a BF on an n-element frame of discernment is presented here.

[1]  Milan Daniel ALGEBRAIC STRUCTURES RELATED TO THE COMBINATION OF BELIEF FUNCTIONS , 2004 .

[2]  Milan Daniel Algebraic Structures Related to Dempster-Shafer Theory , 1994, IPMU.

[3]  Fabio Cuzzolin,et al.  Lp consonant approximation of belief functions in the mass space , 2011 .

[4]  Russell G. Almond Graphical belief modeling , 1995 .

[5]  Philippe Smets,et al.  The Combination of Evidence in the Transferable Belief Model , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  Fabio Cuzzolin On Consistent Approximations of Belief Functions in the Mass Space , 2011, ECSQARU.

[7]  Milan Daniel Distribution of Contradictive Belief Masses in Combination of Belief Functions , 2000 .

[8]  Milan Daniel Probabilistic Transformations of Belief Functions , 2005, ECSQARU.

[9]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[10]  P. Hájek,et al.  A generalized algebraic approach to uncertainty processing in rule-based expert systems (dempsteroids) , 1991 .

[11]  Rolf Haenni Aggregating Referee Scores: an Algebraic Approach , 2008 .

[12]  Weiru Liu,et al.  Analyzing the degree of conflict among belief functions , 2006, Artif. Intell..

[13]  Zied Elouedi,et al.  Towards an Alarm for Opposition Conflict in a Conjunctive Combination of Belief Functions , 2011, ECSQARU.

[14]  Petr Hájek,et al.  Uncertain information processing in expert systems , 1992 .

[15]  Milan Daniel Conflicts within and between Belief Functions , 2010, IPMU.

[16]  R. Yager On the dempster-shafer framework and new combination rules , 1987, Inf. Sci..

[17]  Philippe Smets,et al.  Analyzing the combination of conflicting belief functions , 2007, Inf. Fusion.

[18]  Didier Dubois,et al.  Consonant approximations of belief functions , 1990, Int. J. Approx. Reason..

[19]  Henri Prade,et al.  Representation and combination of uncertainty with belief functions and possibility measures , 1988, Comput. Intell..

[20]  Philippe Smets,et al.  Data association in multi‐target detection using the transferable belief model , 2001, Int. J. Intell. Syst..

[21]  P. P. Shenoy,et al.  On Transforming Belief Function Models to Probability Models , 2003 .