@inbook {5070,
title = {Belief Functions on MV-algebras of Fuzzy Sets: An Overview},
booktitle = {Non-Additive Measures},
volume = {310},
year = {2014},
pages = {173-200},
publisher = {Springer},
organization = {Springer},
abstract = {Belief functions are the measure theoretical objects Dempster-Shafer evidence theory is based on. They are in fact totally monotone capacities, and can be regarded as a special class of measures of uncertainty used to model an agent{\textquoteright}s degrees of belief in the occurrence of a set of events by taking into account different bodies of evidence that support those beliefs. In this chapter we present two main approaches to extending belief func- tions on Boolean algebras of events to MV-algebras of events, modelled as fuzzy sets, and we discuss several properties of these generalized mea- sures. In particular we deal with the normalization and soft-normalization problems, and on a generalization of Dempster{\textquoteright}s rule of combination.},
url = {http://link.springer.com/chapter/10.1007/978-3-319-03155-2_7},
author = {Tommaso Flaminio and Llu{\'\i}s Godo and Tomas Kroupa},
editor = {V. Torra, Y. Narukawa and M. Sugeno}
}
@conference {4724,
title = {Combination and Soft-Normalization of Belief Functions on MV-Algebras},
booktitle = {Modeling Decisions for Artificial Intelligence, MDAI 2012},
volume = {7647},
year = {2012},
pages = {23-34},
publisher = {Springer-Verlag Berlin Heidelberg},
organization = {Springer-Verlag Berlin Heidelberg},
edition = {V. Torra et al.},
address = {Girona (Spain)},
abstract = {Extending the notion of belief functions to fuzzy sets leads to the generalization of several key concepts of the classical Dempster- Shafer theory. In this paper we concentrate on characterizing normalized belief functions and their fusion by means of a generalized Dempster rule of combination. Further, we introduce soft-normalization that arises by either rising up the usual level of contradiction above 0, or by decreasing the classical level of normalization below 1.},
author = {Tommaso Flaminio and Llu{\'\i}s Godo and Tomas Kroupa}
}
@conference {4265,
title = {Characterization of Generalized Necessity Functions in Lukasiewicz Logic},
booktitle = {Nonlinear Mathematics for Uncertainty and Its Applications},
volume = {100},
year = {2011},
pages = {619{\textendash}626},
address = {Beijing, China},
isbn = {978-3-642-22832-2},
author = {Tommaso Flaminio and Tomas Kroupa},
editor = {Li, S. and Wang, X. and Okazaki, Y. and Kawabe, J. and Murofushi, T. and Guan, L.}
}