In this paper we present a generalization of belief functions over fuzzy events. In particular we focus on belief functions defined in the algebraic framework of finite MV-algebras of fuzzy sets. We introduce a fuzzy modal logic to formalize reasoning with belief functions on many-valued events. We prove, among other results, that several different notions of belief functions can be characterized in a quite uniform way, just by slightly modifying the complete axiomatization of one of the modal logics involved in the definition of our formalism.
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[1] http://www.iiia.csic.es/en/individual/tommaso-flaminio-0
[2] http://www.iiia.csic.es/en/individual/lluis-godo
[3] http://www.iiia.csic.es/en/individual/enrico-marchioni-2
[4] http://www.iiia.csic.es/en/publications/keyword/Belief Functions
[5] http://www.iiia.csic.es/en/publications/keyword/Lukasiewicz Logic
[6] http://www.iiia.csic.es/en/publications/keyword/Modal Logics
[7] http://www.iiia.csic.es/en/publications/keyword/Fuzzy Events
[8] http://www.iiia.csic.es/en/publications/export/tagged/4708
[9] http://www.iiia.csic.es/en/publications/export/xml/4708
[10] http://www.iiia.csic.es/en/publications/export/bib/4708
[11] http://www.iiia.csic.es/en/project/arinf
[12] http://www.iiia.csic.es/en/project/at
[13] http://www.iiia.csic.es/en/project/matomuvi
[14] http://www.iiia.csic.es/en/project/tassat