Fuzzy Counterpart of Klein Quadric

Abstract

Many techniques have been proposed to project the high-dimensional space into a low-dimensional space, one of the most famous methods being principal component analysis. The Klein quadric is a geometric shape defined by a second-degree homogeneous equation. The lines of projective three-space are, via the Klein mapping, in one-to-one correspondence with points of a hyperbolic quadric of the projective 5-space. This paper presents a research study on he images under the Klein mapping of the projectice 3-space order of 4 and the fuzzification of the Klein quadric in 5-dimensional projective space.