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Issue:On properties of some IFS operators and operations

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Title of paper: On properties of some IFS operators and operations
Author(s):
Qiongsun Liu
College of Mathematics and Physics, Chongqing University, Chongqing 400044, PR China
Cui Ma
College of Mathematics and Physics, Chongqing University, No.174, Shazheng Road, Shapingba District, Chongqing 400044, PR China
macui4956@163.com
Xiandong Zhou
College of Mathematics and Physics, Chongqing University, Chongqing 400044, PR China
Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 14 (2008) Number 3, pages 17—24
Download:  PDF (148  Kb, File info)
Abstract: The aim of this paper is to point out and correct some errors of two theorems for IFSs in Atanassov (Two theorems for intuitionistic fuzzy sets, Fuzzy Sets and Systems, 2000) and bring forward a new theorem for IFSs. In the end, some elementary, but non-standard equalities between IFSs were formulated.
Keywords: Fuzzy sets, Intuitionistic fuzzy set (IFS), Operator, Operation
References:
  1. K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20(1986) 87-96.
  2. K. Atanassov, More on intuitionistic fuzzy sets, Fuzzy Sets and Systems 33(1) (1989) 37-46.
  3. K. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems 61(2) (1994) 137-142.
  4. K. Atanassov, Remarks on the intuitionistic fuzzy sets. Part 3, Fuzzy Sets and Systems 75(1995) 401-402.
  5. K. Atanassov, An equality between intuitionistic fuzzy sets, Fuzzy Sets and Systems 79 (1996) 257-258.
  6. K. Atanassov, Two theorems for intuitionistic fuzzy sets, Fuzzy Sets and Systems 110 (2000) 267-269.
  7. Supriya Kumar De, Ranjit Biswas, Akhil Ranjan Roy, Some operations on intuitionistic fuzzy sets, Fuzzy Sets and Systems 114 (2000) 477-484.
  8. Dengfeng, Li, Chuntian, Chen, New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognition Letters. 23 (2002) 221-225.
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  10. Weiqiong Wang, Xiaolong Xin. Distance measure between intuitionistic fuzzy sets, Pattern Recognition Letters 26 (2005) 2063-2069.
  11. P. Grzegorzewski, E. Mrowka. Some notes on (Atanassov's) intuitionistic fuzzy sets, Fuzzy Sets and Systems 156 (2005) 492-495.
  12. K. Atanassov, Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade's paper "Terminological difficulties in fuzzy set theory-the case of "Intuitionistic Fuzzy Sets", Fuzzy Sets and Systems 156 (2005) 496-499.
  13. D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk, H. Prade, Are (Atanassov's) intuitionistic fuzzy sets intuitionistic, Fuzzy Sets and Systems, to appear.
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