Abstract

Further results on possibilistic measurement [5, 8, 9] are presented, including the introduction of possibilistic histograms, their interpretation as fuzzy numbers, and their continuous approximations. 1 Possibilistic Measurement Joslyn has presented a measurement method for possibility distributions [5, 8, 9]. The procedure is based on the observations of possibly non-disjoint intervals. From these set statistics an empirical random set can be derived. Under reasonable consistency requirements, its one-point coverage function is a possibility distribution, from which a consonant (possibilistic) random set can in turn be derived. Given a finite universe\Omega := f! i g; 1 i n, the function m: 2\Omega 7! [0; 1] is an evidence function (otherwise known as a basic probability assignment) when m(;) = 0 and P A`\Omega m(A) = 1. Denote a random set generated from an evidence function as S := fh A j ; m j i : m j ? 0g, where h \Delta i is a vector, A j `\Omega ; m j := m(A j ), an...

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