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The management of uncertainty in expert systems has usually been left to adhoc representations and rules of combinations lacking either a sound theory orclear semantics. The objective of this paper is to establish a theoreticalbasis for defining the syntax and semantics of a small subset of calculi ofuncertainty operating on a given term set of linguistic statements oflikelihood. Each calculus is defined by specifying a negation, a conjunctionand a disjunction operator. Families of Triangular norms and conorms constitutethe most general representations of conjunction and disjunction operators.These families provide us with a formalism for defining an infinite number ofdifferent calculi of uncertainty. The term set will define the uncertaintygranularity, i.e. the finest level of distinction among differentquantifications of uncertainty. This granularity will limit the ability todifferentiate between two similar operators. Therefore, only a small finitesubset of the infinite number of calculi will produce notably differentresults. This result is illustrated by two experiments where nine and elevendifferent calculi of uncertainty are used with three term sets containing five,nine, and thirteen elements, respectively. Finally, the use of contextdependent rule set is proposed to select the most appropriate calculus for anygiven situation. Such a rule set will be relatively small since it must onlydescribe the selection policies for a small number of calculi (resulting fromthe analyzed trade-off between complexity and precision).

Selecting Uncertainty Calculi and Granularity: An Experiment in Trading-Off Precision and Complexity