American Institute of Mathematical Sciences

Advanced
October  2006, 2(4): 351-371. doi: 10.3934/jimo.2006.2.351

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, China
2. 

School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia

Received  November 2005 Revised  April 2006 Published  October 2006

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: Decision theory., Fuzzy optimization, Interval number, Interval order relation, Interval arithmetic.
Mathematics Subject Classification: 65G30, 90C70, 90C30, 49M3.
Citation: Bao Qing Hu, Song Wang. A novel approach in uncertain programming part I: new arithmetic and order relation for interval numbers. Journal of Industrial & Management Optimization, 2006, 2 (4) : 351-371. doi: 10.3934/jimo.2006.2.351
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