Study On Fuzzy Vectors On Then-Dimensional Euclidean Space

Based on the corresponding relation between spatial fuzzy points and fuzzy vectors in Euclidean space, this paper discusses the projections and operations of fuzzy vectors.By means of generalizing the definitions of two-dimensional real complanate fuzzy points onto Rn, this paper presents the concept and the representing method by the fuzzy structured element of spatial fuzzy points, as well as the concepts of both same fuzzy points and opposite fuzzy points. Considering the fact that the distance between two points is zero only if they are same, we have revised the axiomatic definition of fuzzy distance given by Buckley, and propose a specific fuzzy distance according to the theory of spherical fuzzy structured element. Because of a lot of curves on the plane can be expressed by relative functional images, so that the paper gives the equations of fuzzy curves on the plane by fuzzy-valued functions, and the way to solve the equation of fuzzy lines presented by Ondrej Pavlacka with fuzzy structured element.Aiming at the corresponding relation between spatial fuzzy points and their projections, this paper regards spatial fuzzy vectors as spherical fuzzy points, builds the one-to-one correspondence between them, gives the representing method of spherical fuzzy vectors by coordinates. At last, it makes a discussion on the operations of spherical fuzzy vectors, including plus and minus, scalar multiplication, inner products, outer products, mixed products, as well as the notion, limitation and some properties of fuzzy-vectored functions.The result not only improves analytical ways of fuzzy geometry of Buckley et.al, but also extends their theories.