Quantum computation techniques for gauging reliability of interval and fuzzy data

Abstract

In traditional interval computations, we assume that the interval data correspond to guaranteed interval bounds, and that fuzzy estimates provided by experts are correct. In practice, measuring instruments are not 100% reliable, and experts are not 100% reliable, we may have estimates which are ‘way off’, intervals which do not contain the actual values at all. Usually, we know the percentage of such outlier un-reliable measurements. However, it is desirable to check that the reliability of the actual data is indeed within the given percentage. The problem of checking (gauging) this reliability is, in general, NP-hard; in reasonable cases, there exist feasible algorithms for solving this problem. In this paper, we show that quantum computation techniques can drastically speed up the computation of reliability of the given data.

Keywords:

• interval uncertainty
• fuzzy uncertainty
• quantum computation
• data reliability

Acknowledgements

This work was partially supported by the Alliances for Graduate Education and the Professoriate (AGEP) grant HRD-0302788 from the National Science Foundation (NSF), by the National Science Foundation grant HRD-0734825 and by Grant 1 T36 GM078000-01 from the National Institutes of Health.

The authors are thankful to Gilles Chabert, Alexandre Goldsztejn, Luc Jaulin and Alasdair Urquhart for their help and encouragement, and to the anonymous referees for valuable suggestions.