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

Pages: 351 - 371, Volume 2, Issue 4, November 2006

doi:10.3934/jimo.2006.2.351       Abstract        Full Text (272.3K)       Related Articles

Bao Qing Hu - School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China (email)
Song Wang - School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia (email)

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.

Keywords:  Interval number, Interval arithmetic, Interval order relation, Fuzzy optimization, Decision theory.
Mathematics Subject Classification:  65G30, 90C70, 90C30, 49M37.

Received: November 2005;      Revised: April 2006;      Published: October 2006.