A novel approach in uncertain programming part I: new arithmetic and order relation for interval numbers

Bao Qing Hu; Song Wang

doi:10.3934/jimo.2006.2.351

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2006, Volume 2, Issue 4: 351-371. Doi: 10.3934/jimo.2006.2.351

This issue Previous Article Next Article A novel approach in uncertain programming part II: a class of constrained nonlinear programming problems with interval objective functions

A novel approach in uncertain programming part I: new arithmetic and order relation for interval numbers

Bao Qing Hu^1, and
Song Wang^2,

1.
School of Mathematics and Statistics, Wuhan University, Wuhan 430072
2.
School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009

Received: October 31, 2005

Revised: March 31, 2006

Published: September 2006

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Abstract

In this paper we propose a new arithmetic and a novel order relation for interval numbers. We shall show that this new interval arithmetic satisfies some operational properties and has the merit that it reduces uncertainties coming from classic ones. We shall also show that the order relation introduced in this paper is a linear or partial order (satisfying reflexivity, anti-symmetry and transitivity), and has the property of comparability. This is in contrast to the existing interval orders which do not have the property of comparability. Numerical examples on profit intervals and uncertain interval data will be presented to demonstrate the usefulness and applicability of these new arithmetic and order relations.

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Mathematics Subject Classification: 65G30, 90C70, 90C30, 49M37.

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