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Publication Details
AFRICAN RESEARCH NEXUS
SHINING A SPOTLIGHT ON AFRICAN RESEARCH
computer science
The set of Hausdorff continuous functions - The largest linear space of interval functions
Reliable Computing, Volume 12, No. 5, Year 2006
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Description
Hausdorff continuous (H-continuous) functions are special interval-valued functions which are commonly used in practice, e.g. histograms are such functions. However, in order to avoid arithmetic operations with intervals, such functions are traditionally treated by means of corresponding semi-continuous functions, which are real-valued functions. One difficulty in using H-continuous functions is that, if we add two H-continuous functions that have interval values at same argument using point-wise interval arithmetic, then we may obtain as a result an interval function which is not H-continuous. In this work we define addition so that the set of H-continuous functions is closed under this operation. Moreover, the set of H-continuous functions is turned into a linear space. It has been also proved that this space is the largest linear space of interval functions. These results make H-continuous functions an attractive tool in real analysis and provides a bridge between real and interval analysis. © Springer 2006.
Authors & Co-Authors
Anguelov, Roumen
South Africa, Pretoria
University of Pretoria
Markov, Svetoslav
Bulgaria, Sofia
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Sendov, Blagovest
Japan, Tokyo
Bulgarian Embassy
Statistics
Citations: 46
Authors: 3
Affiliations: 3
Identifiers
Doi:
10.1007/s11155-006-9006-5
ISSN:
13853139