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Issue:On a generalization of intuitionistic fuzzy graphs: Difference between revisions

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The concept of an [[Intuitionistic fuzzy graph|Intuitionistic Fuzzy Graph]] (IFG) was introduced in 1994 in [9]. It was subsequently an object of some extensions (see [4, 10, 6]), representations (see [2, 3, 5]) and applications (see [5]). Here we discuss a new generalization of the IFGs, using as a basis the concepts of [[Intuitionistic fuzzy sets|Intuitionistic Fuzzy Sets]] (IFSs), [[Intuitionistic fuzzy relations|Intuitionistic Fuzzy Relations]] (IFRs) and [Index matrix[|Index Matrices]] (IMs). All necessary definitions are collected in [5]. We shall introduce only some of the
The concept of an [[Intuitionistic fuzzy graph|Intuitionistic Fuzzy Graph]] (IFG) was introduced in 1994 in [9]. It was subsequently an object of some extensions (see [4, 10, 6]), representations (see [2, 3, 5]) and applications (see [5]). Here we discuss a new generalization of the IFGs, using as a basis the concepts of [[Intuitionistic fuzzy sets|Intuitionistic Fuzzy Sets]] (IFSs), [[Intuitionistic fuzzy relations|Intuitionistic Fuzzy Relations]] (IFRs) and [[Index matrix|Index Matrices]] (IMs). All necessary definitions are collected in [5]. We shall introduce only some of the basic concepts.
basic concepts.


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Revision as of 20:35, 13 December 2015

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Title of paper: On a generalization of intuitionistic fuzzy graphs
Author(s):
Anthony Shannon
KvB Institute of Technology, North Sydney, NSW 2060, Australia
Warrane College, UNSW, P.O. Box 123, Kensington, NSW 1465, Australia
   (current: t.shannon@warrane.unsw.edu.au)
Krassimir Atanassov
CLBME - Bulgarian Academy of Sciences, P.O.Box 12, Sofia- 1113, Bulgaria
krat@bas.bg
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 12 (2006), Number 1, pages 24—29
Download:  PDF (93  Kb, File info)
Abstract: The concept of an Intuitionistic Fuzzy Graph (IFG) was introduced in 1994 in [9]. It was subsequently an object of some extensions (see [4, 10, 6]), representations (see [2, 3, 5]) and applications (see [5]). Here we discuss a new generalization of the IFGs, using as a basis the concepts of Intuitionistic Fuzzy Sets (IFSs), Intuitionistic Fuzzy Relations (IFRs) and Index Matrices (IMs). All necessary definitions are collected in [5]. We shall introduce only some of the basic concepts.


References:
  1. K. Atanassov, Generalized index matrices, Compt. Rend. de l'Academie Bulgare des Sciences, Vol.40, 1987, No 11, 15-18.
  2. Atanassov K., Index matrix representation of the intuitionistic fuzzy graphs, Fifth Scientific Session of the Mathematical Foundations of Artificial Intelligence Seminar, Sofia, Oct. 5, 1994, Preprint MRL-MFAIS-10-94, 36-41.
  3. Atanassov K., On intuitionistic fuzzy graphs and intuitionistic fuzzy relations, Proceedings of the VI IFSA World Congress, Sao Paulo, Brazil, July 1995, Vol. 1, 551-554.
  4. Atanassov K., Temporal intuitionistic fuzzy graphs, Notes on Intuitionistic Fuzzy Sets, Vol. 4 (1998), No. 4, 59-61.
  5. K. Atanassov, Intuitionistic Fuzzy Sets, Springer Physica-Verlag, Berlin, 1999.
  6. Atanassov, K. On index matrix interpretations of intuitionistic fuzzy graphs. Notes on Intuitionistic Fuzzy Sets, Vol. 8 (2002), No. 4, 73-78.
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