On fuzzy projective planes in H^5(2)

In this thesis, the Klein transformation defined from the projective space PG(3,q) to the projective space PG(5,q), and the Klein Quadric obtained by this transformation are studied. Specifically, for q=2 , the points, lines, and planes of the Klein Quadric, denoted as H^2 (2), are examined. The ∝ and β planes of the Klein Quadric in the PG(5,2) projective space and the intersection points of these planes are investigated. Then, based on a maximal flag in PG(5,2), the points of the ∝ and β planes are classified. Using the membership degrees of in the fuzzification of PG(5,2) with respect to this maximal flag, the fuzzification of all ∝ and β planes of the Klein Quadric in PG(5,2) is achieved. Finally, the relations between the fuzzy ∝ and β planes passing through the base point of the fuzzy Klein quadric are determined.