Data Mining, Rough Sets and Granular Computing pp 339349  Cite as
Basic Issues of Computing with Granular Probabilities
Abstract

Imprecision of probabilities is needed to reflect the amount of information on which they are based. The precision should increase with the amount of information available.

Total ignorance can be properly modeled by vacuous probabilities, which are maximally imprecise (i.e., each covers the whole range [0, 1]), but not by any precise probabilities.

Imprecise probabilities are generally easier to assess and elicit than precise ones.

We may be unable to assess probabilities precisely in practice, even if that is possible in principle, because we lack the time and computational ability.

A precise probability model that is defined on some class of events determines only imprecise probabilities for events outside the class.

When several sources of information (sensors, experts, individuals in a group decision) are combined, the extent to which they are consistent can be reflected in the precision of the combined model.
Keywords
Fuzzy Number Bayesian Inference Triangular Membership Function Additivity Axiom Fuzzy IntervalPreview
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