Abstract:
A new type of translation invariant and lower semi continuous fuzzy measure on the
class of subsets of a real Hilbert space is introduced. It measures a subset of the Hilbert
space as a projection of the set along a fixed vector in the Hilbert space. It is proved that
corresponding to each subset of the Hilbert space, the fuzzy measure is determined by
one vector of the Hilbert space. Then it is proved that the fuzzy measure of a closed
convex subset of the Hilbert space can be obtained in terms of two elements of the subset
itself. It is also proved that this fuzzy measure satisfies a condition similar to the null
additivity.
