Operations on Intuitionistic Fuzzy Directed Graphs
Keywords:
Intuitionistic, Fuzzy Graphs, Fuzzy Directed GraphAbstract
The motivation for introducing IFGs is due to The first definition and concept of Intuitionistic Fuzzy Graph (IFG) was introduced. Karunambigai analyzed the properties of minmax IFGs in Shannon and Atanassov defined intuitionistic fuzzy graphs using five types of Cartesian products. In this paper IFGs so defined are named. Some isomorphic properties on IFGs are discussed. et al., discussed the properties of isomorphism on fuzzy graphs and properties of isomorphism on strong fuzzy graphs in which motivated us to develop the same on IFGs and on strong IFGs. The main aim of this study is to build basic definitions of an IFG which will be useful for the researchers for their future study in IFGs. Since the title of the paper is given so. For graph theoretical definitions and throughout this paper all the properties are analyzed for simple minmax IFG.
References
L. A. Zadeh, Toward a generalized theory of uncertainty (GTU) - an outline, Information Sciences, 172 (1 - 2), 2005, 1 - 40.
Ayyaswamy. S,K and Natarajan. C, “Strong (weak) domination in Fuzzy Graphs”, International Journal of Mathematical and Computational Sciences ,Vol 4,No.7,2010,1035-1037.
Berge C, “Graphs and Hyper-graphs”, North-Holland, Amsterdam, 1976.
C. R. Bector and S. Chandra, Fuzzy mathematical programming and fuzzy matrix games, Springer-Verlag, Vol. 169, 2005.
D. Dubois and H. Prade, Fuzzy sets and Systems: Theory and Applications, New York: Academic Press, Vol. 144, 1980.
J. N. Mordeson and P. S. Nair, Fuzzy graphs and fuzzy hyper-graphs, Physica verlag, Heidelberg 1998, Second Edition, 2001.
Rosenfeld, Fuzzy graphs, in: L. A. Zadeh, K.S.Fu, M. Shimura (Eds.), Fuzzy Sets and their Applications to Cognitive and Decision Processes, Academic Press, New York, 1975, 77 - 95.
G. Ausiello, Alessandro D’ Atri, and DomenicoSacca, Strongly equivalent directed hypergraps, Analysis and Design of Algorithms for Combinatorial Problems, Annals of Discrete Mathematics, 25, 1985, 1 - 25.
K. T. Atanassov, G. Pasi and R. Yager, Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making, International Journal of Systems Science, 36 (14), 2005, 859 - 868.
M. R. Berthold and K. P. Huber, Neural network based construction of fuzzy graphs, In Proceedings of the Fourth Annual Conference on Fuzzy Theory and Technology, North Carolina, 1995, 170 - 173.
P. Bhattacharya, Some remarks on fuzzy graphs, Patteren Recognition Let-ters, 6 (5), 1987, 297 - 302.
Sunil Mathew and SunithaM.S, ”Node Connectivity and arc connectivity of a fuzzy graph”, Information Sciences,180(2010)519-531.
S. M. Baas and H. Kwakernaak, Rating and ranking of multiple-aspect alter-natives using fuzzy sets, Automatica, 13 (1), 1977, 47 - 58.
Thilagavathi S, Parvathi R. and Karunambigai M.G, ”Intuitionistic fuzzy hyper-graphs”, J. Cybernetics and Information Technologies, 9(2), (2009), p. 46-53 Sofia.
Wen-Liang Hung, Min-ShenYang,”On Similarity Measures Between Intuitionistic Fuzzy Sets”, International Journal of Intelligent System, Vol 23,364-383.
Yeh R.T and Bang S.Y, “Fuzzy relations, fuzzy graphs, and their applications to clustering analysis”, Fuzzy Sets and their Applications to Cognitive and Decision Processes, pp 125-149,1975.
K. R. Bhutani, On auto-morphisms of fuzzy graphs, Pattern recognition letters, 9 (3), 1989, 159 - 162.
S. M. Baas and H. Kwakernaak, Rating and ranking of multiple-aspect alter-natives using fuzzy sets, Automatica, 13 (1), 1977, 47 - 58.
S. Chen, Ranking fuzzy numbers with maximizing set and minimizing set, Fuzzy Sets and Systems, 17 (2), 1985, 113 - 129.
P. Bhattacharya, Some remarks on fuzzy graphs, Patteren Recognition Let-ters, 6 (5), 1987, 297 - 302.
P. Bhattacharya and F. Suraweera, An Algorithm to compute the max-min powers and a property of fuzzy graphs, Patteren Recognition Letters, 12 (7), 1991, 413 - 420.
This work is licensed under a 