Diagrammatic representation for interval arithmetic

The paper presents a diagrammatic representation of a standard interval space (the so-called “MR-diagram”), and shows how to represent and perform interval arithmetic and derive its various properties using the diagram. The representation is an extension and refinement of the IS-diagram representati...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 324; no. 1; pp. 55 - 80
Main Author Kulpa, Zenon
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.02.2001
Subjects
Diagrammatic reasoning
Diagrammatic representation
Geometric interpretation
Interval arithmetic
Interval space
Interval space
65G40
51M15
Geometric interpretation
00A35
Diagrammatic representation
Interval arithmetic
Diagrammatic reasoning
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Summary:The paper presents a diagrammatic representation of a standard interval space (the so-called “MR-diagram”), and shows how to represent and perform interval arithmetic and derive its various properties using the diagram. The representation is an extension and refinement of the IS-diagram representation devised earlier by the author to represent interval relations. First, the MR-diagram is defined together with appropriate graphical notions and constructions for basic interval relations and operations. Second, diagrammatic constructions for all standard arithmetic operations are presented. Several examples of the use of these constructions to aid reasoning about various simple, though nontrivial, properties of interval arithmetic are included in order to show how the representation facilitates both deeper understanding of the subject matter and reasoning about its properties.
ISSN:0024-3795
1873-1856
DOI:10.1016/S0024-3795(00)00139-7