On the intuitionistic fuzzy projective spaces

In this thesis, intuitionistic fuzzy projective spaces derived from intuitionistic fuzzy vector spaces are examined. In the first two chapters, an introduction to the topic is provided along with the objectives and a literature review. In the third chapter, the fundamental properties of intuitionistic fuzzy vector spaces are discussed; various results are presented on intuitionistic fuzzy vector lines and planes, which are subspaces of these spaces. In the fourth chapter, the intuitionistic fuzzy vector space obtained from the 3-dimensional vector space V and its fundamental properties were examined, and the one and two dimensional intuitionistic fuzzy subspaces are classified. The intuitionistic fuzzy projective plane is determined from the 3-dimensional intuitionistic fuzzy vector space, its intuitionistic fuzzy projective points and lines are defined, and the similarity of intuitionistic fuzzy projective planes to classical projective planes is discussed. In the fifth chapter, after constructing a maximal flag in the 4-dimensional vector space, a 4-dimensional intuitionistic fuzzy vector space is built, and its one, two, and three-dimensional intuitionistic fuzzy subvector spaces are classified. The number of subspaces in each class is determined for the finite field GF(q). Subsequently, an intuitionistic fuzzy projective 3-space is obtained from this structure, its intuitionistic fuzzy projective lines and planes are classified, and the properties of the classical projective 3-space are examined and interpreted in the intuitionistic fuzzy 3-space. In the sixth chapter, by selecting a basis in an n-dimensional vector space and forming a maximal flag, the membership and non-membership degrees of the vectors in the subspaces are defined, thereby constructing an (n+1)-dimensional intuitionistic fuzzy vector space and an n-dimensional intuitionistic fuzzy projective space. In this context, intuitionistic fuzzy projective points, intuitionistic fuzzy projective lines, and hyperplanes are characterized by their membership and non-membership degrees.