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Geometrical aspects of possibility measures on finite domain MV-clans

Geometrical aspects of possibility measures on finite domain MV-clans
Geometrical aspects of possibility measures on finite domain MV-clans
In this paper, we study generalized possibility and necessity measures on MV-algebras of [0, 1]-valued functions (MV-clans) in the framework of idempotent mathematics, where the usual field of reals ℝ is replaced by the max-plus semiring ℝ max We prove results about extendability of partial assessments to possibility and necessity measures, and characterize the geometrical properties of the space of homogeneous possibility measures. The aim of the present paper is also to support the idea that idempotent mathematics is the natural framework to develop the theory of possibility and necessity measures, in the same way classical mathematics serves as a natural setting for probability theory. © 2012 Springer-Verlag.
Idempotent mathematics, MV-algebras, Max-plus convexity, Possibility measures
1863-1873
Flaminio, Tommaso
10824669-cfbb-4724-aa74-e1b31574dae8
Godo, Lluís
0518f088-84ec-4816-ad43-4e240ae66dc1
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96
Flaminio, Tommaso
10824669-cfbb-4724-aa74-e1b31574dae8
Godo, Lluís
0518f088-84ec-4816-ad43-4e240ae66dc1
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96

Flaminio, Tommaso, Godo, Lluís and Marchioni, Enrico (2012) Geometrical aspects of possibility measures on finite domain MV-clans. Soft Computing, 16 (11), 1863-1873. (doi:10.1007/s00500-012-0838-0).

Record type: Article

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 idempotent mathematics, where the usual field of reals ℝ is replaced by the max-plus semiring ℝ max We prove results about extendability of partial assessments to possibility and necessity measures, and characterize the geometrical properties of the space of homogeneous possibility measures. The aim of the present paper is also to support the idea that idempotent mathematics is the natural framework to develop the theory of possibility and necessity measures, in the same way classical mathematics serves as a natural setting for probability theory. © 2012 Springer-Verlag.

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e-pub ahead of print date: 11 February 2012
Published date: November 2012
Keywords: Idempotent mathematics, MV-algebras, Max-plus convexity, Possibility measures

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Local EPrints ID: 416590
URI: http://eprints.soton.ac.uk/id/eprint/416590
PURE UUID: 1252f1f2-5abf-4385-9082-e0e4d945bf33

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Date deposited: 03 Jan 2018 17:30
Last modified: 13 Mar 2019 19:04

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Contributors

Author: Tommaso Flaminio
Author: Lluís Godo
Author: Enrico Marchioni

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