Abstract
We study a generalization of necessity functions to MV-algebras. In particular, we are going to study belief functions whose associated mass assignments have nested focal elements. Since this class of belief functions coincides with necessity functions on Boolean algebras, we will call them generalized necessity functions. Using geometrical and combinatorial techniques we provide several characterizations of these functions in terms of Choquet integral, Lebesgue integral, and min-plus polynomials.
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Flaminio, T., Kroupa, T. (2011). Characterization of Generalized Necessity Functions in Łukasiewicz Logic. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_75
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DOI: https://doi.org/10.1007/978-3-642-22833-9_75
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