On fuzzy n-cell numbers and n-dimension fuzzy vectors

Fuzzy n-cell numbers are a kind of special n-dimension fuzzy numbers, whose sets of cuts are all hyperrectangles. n-dimension fuzzy vectors are the Cartesian products of n one-dimension fuzzy numbers. In this paper, we show that the fuzzy n-cell number space and the n-dimension fuzzy vector space are identical, and obtain the relations of the joint membership function and the edge membership functions of a fuzzy n-cell number (i.e. a n-dimension fuzzy vector). Using fuzzy vector form representations of fuzzy n-cell numbers, we study the metric (of two fuzzy n-cell numbers), the supremum (of a set of fuzzy n-cell numbers) and operational rules (of addition, scalar multiplication and multiplication) of fuzzy n-cell numbers, and get the fuzzy vector form characterizations of the differentiability, measurability and integrability of fuzzy n-cell number valued fuzzy mappings.