TitleGeometrical aspects of possibility measures on finite domain MV-clans
Publication TypeJournal Article
Year of Publication2012
AuthorsFlaminio T, Godo L, Marchioni E
JournalSoft Computing - A Fusion of Foundations, Methodologies and Applications

In this paper we study generalized possibility and necessity measures on MV-algebras of $[0, 1]$-valued functions (MV-clans) in the framework of the so-called idempotent mathematics, where the usual field of reals $\mathbb{R}$ is replaced by the {\em max-plus} semiring $\mathbb{R}_{\max}$. We prove results about extendability of partial assessments to possibility and necessity measures, and we characterize the geometrical properties of the space of homogeneous possibility measures. Not secondarily, the aim of the present paper is also to support the idea that idempotent mathematics is the natural framework where to develop possibility and necessity theory, in the same way classical mathematics serve as a natural setting for probability theory.