A Novel Approach in Uncertain Programming Part I: New Arithmetic and Order relation for Interval Numbers

B.Q. Hu, Song Wang

    Research output: Contribution to journalArticle

    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 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.
    Original languageEnglish
    Pages (from-to)351-371
    JournalJournal of Industrial and Management Optimization
    Volume2
    Issue number4
    Publication statusPublished - 2006

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