  In this note - starting from $d$-dimensional (with $d>1$) fuzzy vectors - we
prove Donsker's classical invariance principle. We consider a fuzzy random walk
${S^*_n}=X^*_1+\cdots+X^*_n,$ where $\{X^*_i\}_1^{\infty}$ is a sequence of
mutually independent and identically distributed $d$-dimensional fuzzy random
variables whose $\alpha$-cuts are assumed to be compact and convex. Our
reasoning and technique are based on the well known conjugacy correspondence
between convex sets and support functions, which allows for the association of
an appropriately normalized and interpolated time-continuous fuzzy random
process with a real valued random process in the space of support functions. We
show that each member of the associated family of dual sequences tends in
distribution to a standard Brownian motion.

Probability