On consistent belief functions

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

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

  AUTHOR = "Fabio Cuzzolin", 
  TITLE = "On consistent belief functions",
  JOURNAL = "to submit to the IEEE Transactions on SMC - part B", 
  YEAR = "2011"