Fabio Cuzzolin To submit to the IEEE Transactions on Fuzzy Systems, 2011 Abstract In this paper solve the problem of approximating a belief measure with a necessity measure or "consonant belief function" in a convex geometric framework. Consonant belief functions form a simplicial complex in the space of all belief functions. As necessity measures are strictly related to the L1 norm it makes sense to look for approximations which minimize Lp norms. Partial approximations are first sought in each simplicial component of the consonant complex, while global solutions are obtained from the set of such partial ones. The obtained Lp consonant approximations are discussed and their interpretation in terms of degrees of belief provided. sp  Download PDF  Zipped Postscript BibTeX entry @article{cuzzolin11tfs,    AUTHOR = "Fabio Cuzzolin",    TITLE = "Consonant approximations of belief functions through Lp norms",   JOURNAL = "to submit to the IEEE Transactions on Fuzzy Systems",    YEAR = "2011"  }