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Measuring Uncertainty Without a Norm

Werschulz, Arthur G.

Traub, Wasilkowski, and Wozniakowski have shown how uncertainty can be defined and analyzed without a norm or metric. Their theory is based on two natural and non-restrictive axioms. We show that these axioms induce a family of pseudometrics, and that balls of radius E are (roughly) the E-approximations to the solution. In addition, we show that a family of pseudometrics is necessary, even for the problem of computing x such that | f(x) | < E , where f is a real function.

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Academic Units
Computer Science
Publisher
Department of Computer Science, Columbia University
Series
Columbia University Computer Science Technical Reports, CUCS-035-82
Published Here
October 26, 2011