Dealing with Uncertainties in Computing: from Probabilistic and
Interval Uncertainty to Combination of Different Approaches, with
Application to Geoinformatics, Bioinformatics, and Engineering

Vladik Kreinovich
Department of Computer Science,
University of Texas at El Paso
El Paso, Texas 79968, USA
vladik@utep.edu

Most data processing techniques traditionally used in scientific and
engineering practice are statistical. These techniques are based on
the assumption that we know the probability distributions of
measurement errors etc.

In practice, often, we do not know the distributions, we only know the
bound D on the measurement accuracy -- hence, after the get the
measurement result X, the only information that we have about the
actual (unknown) value x of the measured quantity is that $x$ belongs
to the interval [X - D, X + D]. Techniques for data processing under
such interval uncertainty are called interval computations; these
techniques have been developed since 1950s.

In many practical problems, we have a combination of different types
of uncertainty, where we know the probability distribution for some
quantities, intervals for other quantities, and expert information for
yet other quantities.

There exist a lot of theoretical research and practical applications
in dealing with these types of uncertainty: interval, fuzzy, and
combined. However, even for the simplest basic data processing
techniques, it is often still necessary to undertake a lot of research
to transit from probabilistic to interval and fuzzy uncertainty.

The purpose of this talk is to describe the theoretical background for
interval and combined techniques, to describe the existing practical
applications, and ideally, to come up with a roadmap for such
techniques.

We start with the problem of chip design in computer engineering. In
this problem, traditional interval methods lead to estimates with
excess width. The reason for this width is that often, in addition to
the intervals of possible values of inputs, we also have partial
information about the probabilities of different values within these
intervals -- and standard interval techniques ignore this information.

It is therefore desirable to extend interval techniques to the
situations when, in addition to intervals, we also have a partial
probabilistic information. In the talk, we give a brief overview of
these techniques, and we emphasize the following three application
areas: computer engineering, bioinformatics, and geoinformatics.
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