Fuzzy projective geometries

In and we introduced a rst model of fuzzy projective geometries deduced from respectively fuzzy vector spaces and fuzzy groups This provided a link between the fuzzy versions of classical theories that are very closely related However the geometric structure involved in this model is rather weak a fuzzy projec tive space in this sense is equivalent with a given se quence of subspaces in the base projective space In another fuzzy model of projective geometries was constructed bred projective planes In this model the role of points and lines is equivalent this is not the case in the rst model as in the classical case Points and lines of the base geometry mostly have multiple degrees of membership This paper introduces a third model We rst de ne a fuzzy projective plane in which points and lines play the same role and such that every point and every line in the base plane possess only one degree