Strong distance in fuzzy graphs is introduced in this article. With respect to these distances, the concepts of center and self centered fuzzy graphs are introduced and their properties are discussed. A characterization for self centered fuzzy graphs using the max - max composition of the corresponding distance matrices is obtained. Central properties of fuzzy trees and blocks are also discussed.
AnjalyN. and MathewS., On blocks and stars in fuzzy graphs, Journal of Intelligent and Fuzzy Systems28 (2015), 1659–1665.
2.
BhutaniK.R., On automorphisms of fuzzy graphs, Pattern Recognition Letters9 (1989), 159–162.
3.
BhutaniK.R. and RosenfeldA., Fuzzy end nodes in fuzzy graphs, Information Sciences152 (2003), 323–326.
4.
BhutaniK.R. and RosenfeldA., Geodesics in fuzzy graphs, Electronic Notes in Discrete Mathematics15 (2003), 51–54.
5.
BhutaniK.R. and RosenfeldA., Strong arcs in fuzzy graphs, Information Sciences152 (2003), 319–322.
6.
BiglarbegianA., SadeghianW. and MelekM., On the accessability/controllability of fuzzy control systems, Information Sciences202 (2012), 58–72.
7.
BustinceH., BarrenecheaE., FernandezJ., PagolaM., MonteroJ. and GuerraC., Contrast of a fuzzy relation, Information Sciences180 (2010), 1326–1344.
8.
BustinceH., BeliakovG., GoswamiD., MukherjeeU. and PalN., On averaging operators for Atanassov’s intuitionistic fuzzy sets, Information Sciences181 (2011), 1116–1124.
9.
ChenD., HuQ. and YangY., Parameterized attribute reduction with Gaussian kernel based fuzzy rough sets, Information Sciences181(23) (2011), 5169–5179.
10.
GactoM.J., AlcalaR. and HerreraF., Interpretability of Linguistic fuzzy rule-based systems: An overview of interpretability measures, Information Sciences181(20) (2011), 4340–4360.
MordesonJ.N. and NairP.S.Fuzzy Graphs and Fuzzy Hypergraphs, Physica -Verlag, Newyork, 2000.
13.
HuQ., YuD. and GuoM., Fuzzy preference based rough sets, Information Sciences180(10) (2010), 2003–2022.
14.
HuQ., AnS. and
DarenYu, Soft fuzzy dependency for robust feature evaluation, Information Sciences180 (2010), 4384–4400.
15.
RosenfeldA., Fuzzy graphs, In:
ZadehL.A.,
FuK.S. and
ShimuraM. (Eds), Fuzzy sets and their Applications to Cognitive and Decision Processes, Academic Press, New York, 1975, pp. 77–95.
16.
Ruey-Jing Lian, Grey-prediction self-organizing fuzzy controller for robotic motion control, Information Sciences202 (2012), 73–89.
17.
SanzJ., FernandezA., BustinceH. and HerreraF., Improving the performance of fuzzy rule-based classification systems with interval-valued fuzzy sets and genetic amplitude tuning, Information Sciences180 (2010), 3674–3685.
18.
MathewSunil and SunithaM.S., Types of arcs in a fuzzy graph, Information Sciences179 (2009), 1760–1768.
19.
MathewSunil and SunithaM.S., Node connectivity and arc connectivity of a fuzzy graph, Information Sciences180 (2010), 519–531.
20.
SunithaM.S. and VijayakumarA., A characterization of fuzzy trees, Information Sciences113 (1999), 293–300.
21.
SunithaM.S., VijayakumarA., Some metric aspects of fuzzy graphs, In:
BalakrishnaR.,
MulderH.M.,
VijayakumarA. (Eds), Proceedings of the Conference on Graph Connections CUSAT, Allied Publishers, Cochin, 1999, pp. 111–114.
22.
SunithaM.S. and VijayakumarA., Complement of a fuzzy graph, Indian Journal of Pure and Applied Mathematics33 (2002), 1451–1464.
23.
SunithaM.S. and VijayakumarA., Blocks in fuzzy graphs, The Journal of Fuzzy Mathematics13 (2005), 13–23.
24.
YehR.T. and BangS.Y., Fuzzy relations, fuzzy graphs and their applications to clustering analysis, In:
ZadehL.A.,
FuK.S. and ShimuraM. (Eds), Fuzzy Sets and Their Applications, Academic Press, 1975, pp. 125–149.
25.
ZadehL.A., Fuzzy sets, Information and Control8 (1965), 338–353.
26.
ZadehL.A., Is there a need for fuzzy logic?Information Sciences178 (2008), 2751–2779.
