A Granular Semantics for Fuzzy Measures and its Application to Climate Change Scenarios

A granular based semantics for fuzzy measures is introduced in which the measure of a set of propositions approximates the probability of the disjunction of these propositions. This approximation is derived from known probabilities across a granular partition of the set of possible worlds. This interpretation is then extended to allow for the case where there is uncertainty regarding the meanings of propositions. Such a semantics is motivated by, and provides some justification for, the use of fuzzy measures to quantify the uncertainty associated with climate emissions scenarios. The use of socio-economic scenarios in climate models is discussed in the context of a possible worlds model and an example is given of the use of fuzzy measures across scenarios to aggregate global mean temperature predictions.