The representation of uncertain information and inference with such information
are some of the fundamental issues in uncertainty management. Conventional methods
for uncertainty management usually use a single value with the exception of
interval-based approaches. In interval-based approaches, an interval is used to represent
the uncertain information. It is assumed that the true, possibly unknown, value
lies in an interval. However, in order to use interval-based methods, there must exist
an order relation on the set of data values.
The main objective of this thesis is to extend single-valued and interval-valued
methods by introducing a framework of set-valued computations. In this model,
uncertain information is described by a set without any further restrictions. Basic
issues of set-based computations are investigated. Operations on set values are defined
based on the corresponding point-based (i.e., single-value-based) operations on their
members. The properties of set-based computations are examined in connection to
the corresponding properties of the point-based computations. Within the proposed
framework, a critical analysis of a number of existing set-based computation methods
is presented. This provides further evidence supporting the proposed model. To a
large extent, the present study may be regarded as a more explicit re-examination of
methods that have been implicitly used in many studies, using a unified notion. The
results of such an investigation will be useful in establishing a framework for more
systematic study of set-based computations
