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Interval-valued fuzzy graphs. (English) Zbl 1211.05133

Summary: We define the Cartesian product, composition, union and join on interval-valued fuzzy graphs and investigate some of their properties. We also introduce the notion of interval-valued fuzzy complete graphs and present some properties of self-complementary and self-weak complementary interval-valued fuzzy complete graphs.

MSC:

05C72 Fractional graph theory, fuzzy graph theory
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[1] Zadeh, L.A., The concept of a linguistic and application to approximate reasoning I, Inf. sci., 8, 199-249, (1975) · Zbl 0397.68071
[2] Zadeh, L.A., Fuzzy sets, Inf. control, 8, 338-353, (1965) · Zbl 0139.24606
[3] Mendel, J.M., Uncertain rule-based fuzzy logic systems: introduction and new directions, (2001), Prentice-Hall Upper Saddle River, New Jersey · Zbl 0978.03019
[4] Gorzalczany, M.B., A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy sets syst., 21, 1-17, (1987) · Zbl 0635.68103
[5] Gorzalczany, M.B., An interval-valued fuzzy inference method some basic properties, Fuzzy sets syst., 31, 243-251, (1989)
[6] Roy, M.K.; Biswas, R., I-V fuzzy relations and sanchez’s approach for medical diagnosis, Fuzzy sets syst., 47, 35-38, (1992) · Zbl 0850.04003
[7] Turksen, I.B., Interval valued fuzzy sets based on normal forms, Fuzzy sets syst., 20, 191-210, (1986) · Zbl 0618.94020
[8] Rosenfeld, A., Fuzzy graphs, (), 77-95
[9] Bhattacharya, P., Some remarks on fuzzy graphs, Pattern recognit. lett., 6, 297-302, (1987) · Zbl 0629.05060
[10] Mordeson, J.N.; Peng, C.S., Operations on fuzzy graphs, Inf. sci., 79, 159-170, (1994) · Zbl 0804.05069
[11] Mordeson, J.N.; Nair, P.S., Fuzzy graphs and fuzzy hypergraphs, (1998), Physica Verlag Heidelberg, Second edition 2001 · Zbl 0905.68095
[12] Sunitha, M.S.; Vijayakumar, A., Complement of a fuzzy graph, Indian J. pure appl. math., 33, 1451-1464, (2002) · Zbl 1013.05081
[13] Bhutani, K.R.; Battou, A., On \(M\)-strong fuzzy graphs, Inf. sci., 155, 103-109, (2003) · Zbl 1033.05095
[14] Bhutani, K.R.; Rosenfeld, A., Strong arcs in fuzzy graphs, Inf. sci., 152, 319-322, (2003) · Zbl 1040.03518
[15] J. Hongmei, W. Lianhua, Interval-valued fuzzy subsemigroups and subgroups sssociated by intervalvalued suzzy graphs, in: 2009 WRI Global Congress on Intelligent Systems, 2009, pp. 484-487.
[16] Akram, M., Fuzzy Lie ideals of Lie algebras with interval-valued membership functions, Quasigroups related systems, 16, 1-12, (2008) · Zbl 1195.17023
[17] Akram, M.; Dar, K.H., Generalized fuzzy \(K\)-algebras, ISBN: 978-3-639-27095-2, (2010), VDM Verlag, pp. 288 · Zbl 1113.06014
[18] Alaoui, A., On fuzzification of some concepts of graphs, Fuzzy sets syst., 101, 363-389, (1999) · Zbl 0934.05099
[19] Atanassov, K.T., Intuitionistic fuzzy sets: theory and applications, studies in fuzziness and soft computing, Physica-verl., (1999) · Zbl 0939.03057
[20] Harary, F., Graph theory, (1972), Addison-Wesley Reading, MA · Zbl 0797.05064
[21] K.P. Huber, M.R. Berthold, Application of fuzzy graphs for metamodeling, in: Proceedings of the 2002 IEEE Conference, pp. 640-644.
[22] Mathew, S.; Sunitha, M.S., Node connectivity and arc connectivity of a fuzzy graph, Inf. sci., 180, 4, 519-531, (2010) · Zbl 1233.05163
[23] Mordeson, J.N., Fuzzy line graphs, Pattern recognit. lett., 14, 381-384, (1993) · Zbl 0785.05069
[24] Nagoorgani, A.; Radha, K., Isomorphism on fuzzy graphs, Int. J. comput. math. sci., 2, 190-196, (2008) · Zbl 1153.05310
[25] Perchant, A.; Bloch, I., Fuzzy morphisms between graphs, Fuzzy sets syst., 128, 149-168, (2002) · Zbl 1005.05041
[26] Zadeh, L.A., Similarity relations and fuzzy orderings, Inf. sci., 3, 177-200, (1971) · Zbl 0218.02058
[27] Bhutani, K.R., On automorphism of fuzzy graphs, Pattern recognit. lett., 9, 159-162, (1989) · Zbl 0800.68740
[28] Mendel, J.M.; Gang, X., Fast computation of centroids for constant-width interval-valued fuzzy sets, fuzzy information processing society, Nafips, 621-626, (2006)
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