A hyperspatial representation of a particular set of fuzzy preference relations

In this paper we study a geometrical representation of a special class of fuzzy preference relations by establishing a one-one correspondence between the set of all these relations and a hypercube of an n(n?1)/2 dimensional space.Furthermore, we study some geometrical figures (called H-spheres) and properties of the points which represent the preference relations in the above mentioned euclidean space.