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. © 2009 Wiley Periodicals, Inc.

[1]  Janusz Kacprzyk,et al.  Distances between intuitionistic fuzzy sets , 2000, Fuzzy Sets Syst..

[2]  Miin-Shen Yang,et al.  On similarity measures between intuitionistic fuzzy sets , 2008, Int. J. Intell. Syst..

[3]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[4]  Chris Cornelis,et al.  Intuitionistic fuzzy sets and interval-valued fuzzy sets: a critical comparison , 2003, EUSFLAT Conf..

[5]  K. Atanassov.  More on intuitionistic fuzzy sets , 1989 .

[6]  Janusz Kacprzyk,et al.  A New Similarity Measure for Intuitionistic Fuzzy Sets: Straightforward Approaches may not work , 2007, 2007 IEEE International Fuzzy Systems Conference.

[7]  Eulalia Szmidt,et al.  Assigning the parameters for intuitionistic fuzzy sets , 2005 .

[8]  Joan Y. Chiao,et al.  Mental representations of social status , 2004, Cognition.

[9]  Janusz Kacprzyk,et al.  Multistage evolutionary optimization of fuzzy systems—application to optimal fuzzy control , 1997 .

[10]  J. Baldwin,et al.  Entropy for Intuitionistic Fuzzy, Set Theory and Mass Assignment Theory , 2004 .

[11]  Miin-Shen Yang,et al.  Fuzzy entropy on intuitionistic fuzzy sets , 2006, Int. J. Intell. Syst..

[12]  Janusz Kacprzyk,et al.  A New Concept of a Similarity Measure for Intuitionistic Fuzzy Sets and Its Use in Group Decision Making , 2005, MDAI.

[13]  I. Turksen.  Interval valued fuzzy sets based on normal forms , 1986 .

[14]  Humberto Bustince,et al.  Vague sets are intuitionistic fuzzy sets , 1996, Fuzzy Sets Syst..

[15]  Zeshui Xu,et al.  Some geometric aggregation operators based on intuitionistic fuzzy sets , 2006, Int. J. Gen. Syst..

[16]  Etienne E. Kerre,et al.  On the relationship between some extensions of fuzzy set theory , 2003, Fuzzy Sets Syst..

[17]  W. Levelt,et al.  Semantic distance effects on object and action naming , 2002, Cognition.

[18]  Guo-Jun Wang,et al.  Intuitionistic fuzzy sets and L-fuzzy sets , 2000, Fuzzy Sets Syst..

[19]  H. Carter.  Fuzzy Sets and Systems — Theory and Applications , 1982 .

[20]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[21]  D. Dubois,et al.  Fuzzy Sets: History and Basic Notions , 2000 .