On the packing density of a fuzzy set (Q1842390)

By a membership function of a fuzzy subset \(A\) of \(\mathbb{R}^n\) a function \(u_A : \mathbb{R}^n \to [0, \infty]\) is understood. If \(\sum^N_{j = 1} u_{K_j} (t) \leq u_G (t)\) then the density of \(G\) by \(K_1, \ldots, K_N\) is the number \(d = (\int_{R^n} u_G (t) dt)^{- 1}\) \((\sum^N_{j = 1} \int_{R^n} u_{K_j} (t)dt)\). In the paper some lower and upper bounds for the density are given based on a Fourier transform.