A novel approach in uncertain programming - Part I: New arithmetic and order relation for interval numbers

作者：Hu Bao Qing^*; Wang Song

来源：Journal of Industrial and Management Optimization, 2006, 2(4): 351-371.

• interval number
• interval arithmetic
• interval order relation
• fuzzy optimization
• decision theory

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 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.

• 出版日期2006-11
• 单位武汉大学