Belief functions on MV-algebras of fuzzy events based on fuzzy evidence

Authors:
T. Flaminio;L. Godo;E. Marchioni
Affiliations:
IIIA, Artificial Intelligence Research Institute, Spanish National Research Council, Bellaterra, Spain;IIIA, Artificial Intelligence Research Institute, Spanish National Research Council, Bellaterra, Spain;IIIA, Artificial Intelligence Research Institute, Spanish National Research Council, Bellaterra, Spain
Venue:
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
Year:
2011

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Abstract

Recently Kroupa has proposed a generalization of belief functions on MV-algebras, the latter being the chosen algebraic setting for fuzzy (or many-valued) events. However, Kroupa's belief functions evaluate the degree of belief in the occurrence of fuzzy events by taking into account (weighted) evidence on classical subsets. In other words, the focal elements, used in determining the degree of belief, are classical sets. Within the MV-algebraic setting, the aim of the present work is to introduce a generalization of Kroupa belief functions that allows to deal with fuzzy events supported by evidence on fuzzy subsets.