GENERALIZED POSSIBILITY MEASURES

We define a generalized possibility measure (GPM) on a set X to be a f unction from the power set of X to the unit interval I = [0, 1], where by the measure of a finite union of subsets of X equals the maximum of their measures. We characterize GPMs as the infima of downward direct ed families of possibility measures. This helps to confer an intuitive meaning or GPMs. We discuss all directed families of possibility meas ures (or, equivalently, of possibility distributions) which generate a given GPM, and we identify the largest such family. We introduce exte nsions of GPMs to real functions on I(X), obtained through a continuou s triangular norm. We provide characterizations and alternative descri ptions for those extensions.