Notation in Interval Analysis

Publications in interval analysis currently suffer from a multitude of incompatible notational styles. There are obvious advantages in a standardized notation, especially for those peripheral to our field who only want to read an occasional paper to see whether the field offers something for the solution of their problems. It is important for the future of interval analysis to reach out to these colleagues; this proposal of a standardized notation is to limit the burden of learning new notation to a minimum.

In much of mathematics, standardization happens automatically because people use the notation introduced by the first influential papers on an issue. In interval analysis, this unfortunately did not happen. Worse, because there was no consensus in the past literature, new authors of work in interval analysis created their own notational habits, and produced further variants that added to the confusion. The time seems ripe to attempt to correct this unpleasant situation.

Here a standard is proposed that hopefully persuades the entire community to use it for publishing their work. Emphasis is on easy usage and easy comprehensibility.

The proposed standard is based on the following guiding lines: The notation should blend seamlessly with traditional notation in mathematics, in particular numerical analysis and optimization. It should also result in formulas that look as simple as possible, while conveying the meaning clearly even to readers not working in the field. And it should create a minimal burden in preparing manuscripts for authors wanting to conform to the standard. In particular, standardization is restricted to the most basic aspects of interval terminology.

We hope that the suggested notation will appear persuasive to authors in interval analysis and its applications, convincing them that using it is likely to improve the communication of ideas in interval analysis to colleagues and potential users.

To facilitate the acceptance of the proposed standard, a LaTeX style file is provided, together with the LaTeX source of the paper describing the standard as an example of its use, that makes it easy to create documents conforming to the standard. The style file is designed to keep the LaTeX notation for intervals as simple as possible. (Note that some of the macros may overwrite macros from some other packages -- redefine these macros if necessary.)

Interval Analysis

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