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Intuitionistic fuzzy sets: Spherical representation and distances
Author(s) -
Yang Y.,
Chiclana F.
Publication year - 2009
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.20342
Subject(s) - mathematics , representation (politics) , interpretation (philosophy) , fuzzy logic , plane (geometry) , surface (topology) , fuzzy set , algebra over a field , pure mathematics , discrete mathematics , algorithm , artificial intelligence , computer science , geometry , politics , political science , law , programming language
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. © 2009 Wiley Periodicals, Inc.