Intuitionistic fuzzy sets: Spherical representation and distances

Most existing distances between intuitionistic fuzzy sets are defined in linear plane representations in 2D or 3D space. Here, we define a new interpretation of intuitionistic fuzzy sets as a restricted spherical surface in 3D space. A new spherical distance for intuitionistic fuzzy sets is introduced. We prove that the spherical distance is different from those existing distances in that it is nonlinear with respect to the change of the corresponding fuzzy membership degrees. C © 2009 Wiley Periodicals, Inc.