Selecting Uncertainty Calculi and Granularity: An Experiment in
  Trading-Off Precision and Complexity
  The management of uncertainty in expert systems has usually been left to ad
hoc representations and rules of combinations lacking either a sound theory or
clear semantics. The objective of this paper is to establish a theoretical
basis for defining the syntax and semantics of a small subset of calculi of
uncertainty operating on a given term set of linguistic statements of
likelihood. Each calculus is defined by specifying a negation, a conjunction
and a disjunction operator. Families of Triangular norms and conorms constitute
the most general representations of conjunction and disjunction operators.
These families provide us with a formalism for defining an infinite number of
different calculi of uncertainty. The term set will define the uncertainty
granularity, i.e. the finest level of distinction among different
quantifications of uncertainty. This granularity will limit the ability to
differentiate between two similar operators. Therefore, only a small finite
subset of the infinite number of calculi will produce notably different
results. This result is illustrated by two experiments where nine and eleven
different calculi of uncertainty are used with three term sets containing five,
nine, and thirteen elements, respectively. Finally, the use of context
dependent rule set is proposed to select the most appropriate calculus for any
given situation. Such a rule set will be relatively small since it must only
describe the selection policies for a small number of calculi (resulting from
the analyzed trade-off between complexity and precision).
