Publication Type:
Journal Article
Source:
Soft Computing - A Fusion of Foundations, Methodologies and Applications, Springer, Volume 16, Issue 11, p.1863-1873 (2012)
URL:
http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s00500-012-0838-0
Abstract:
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.
