The construction of consistent possibility and necessity measures
Given a general measure mu (finite or infinite), we develop possibility and necessity measures as upper and lower estimators of mu. We provide a method for constructing such fuzzy measures and show that the measure can be approximated with arbitrary closeness using fuzzy measures constructed this way. Using the extension principle, these consistent possibility and necessity measures are used to produce possibility and necessity measures on the range space of a measurable function which are consistent with the measure on the range space induced by the measurable function. This induced measure can be approximated with arbitrary closeness by extending consistent possibility and necessity measures constructed on the domain space. (C) 2002 Elsevier Science B.V. All rights reserved.
possibility theory non-additive measures measure theory