Fabio Cuzzolin 
To submit to the IEEE Transactions on SMC  part B, 2011 

Abstract 
In this paper we define the class of consistent belief functions as the counterparts of consistent knowledge bases in classical logic. We prove that such class can be defined univocally no matter our
definition of proposition implied by a belief function. As consistency can be desirable in decision
making, the problem of transforming an arbitrary belief function into a consistent one arise, and can be
posed in a geometric setup. We prove that consistent belief functions live on a structured collection of
simplices called simplicial complex. Eventually, we show how each belief function naturally decomposes
into consistent components on such a complex, in a fashion which recalls the pignistic transform. 
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BibTeX entry 
@article{cuzzolin11smcb,
AUTHOR = "Fabio Cuzzolin",
TITLE = "On consistent belief functions",
JOURNAL = "to submit to the IEEE Transactions on SMC  part B",
YEAR = "2011"
} 
