Abstract
In this chapter, we present fundamental and technical concepts like fuzzy hypergraphs, fuzzy column hypergraphs, fuzzy row hypergraphs, fuzzy competition hypergraphs, fuzzy k-competition hypergraphs, fuzzy neighborhood hypergraphs, and \({\mathscr {N}}\)-hypergraphs. We describe applications of fuzzy competition hypergraphs in decision support systems, including predator–prey relations in ecological niches, social networks, and business marketing. Further, we introduce complex fuzzy hypergraphs, \(\mu e^{i\theta }\)-level hypergraphs, covering constructions, 2-sections, and \(L_2\)-sections of these hypergraphs.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Abdul-Jabbar, N., Naoom, J.H., Ouda, E.H.: Fuzzy dual graph. J. Al-Nahrain Univ. 12(4), 168–171 (2009)
Akram, M.: Studies in Fuzziness and Soft Computing. Fuzzy Lie algebras, vol. 9, pp. 1–302. Springer, Berlin (2018)
Akram, M., Alshehri, N.O.: Tempered interval-valued fuzzy hypergraphs. Sci. Bull. Ser. A Appl. Math. Phys. 77(1), 39–48 (2015)
Akram, M., Chen, W.J., Davvaz, B.: On \({\cal{N}}\)-hypergraphs. J. Intell. Fuzzy Syst. 26, 2937–2944 (2014)
Berge, C.: Graphs and Hypergraphs. North-Holland, Amsterdam (1973)
Craine, M.W.L.: Fuzzy hypergraphs and fuzzy intersection graphs. University of Idaho, Ph.D Thesis (1993)
Goetschel Jr., R.H.: Introduction to fuzzy hypergraphs and Hebbian structures. Fuzzy Sets Syst. 76, 113–130 (1995)
Goetschel Jr., R.H.: Fuzzy colorings of fuzzy hypergraphs. Fuzzy Sets Syst. 94, 185–204 (1998)
Goetschel Jr., R.H., Craine, W.L., Voxman, W.: Fuzzy transversals of fuzzy hypergraphs. Fuzzy Sets Syst. 84, 235–254 (1996)
Jun, Y.B., Lee, K.J., Song, S.Z.: \({\cal{N}}\)-ideals of \(BCK/BCI\)-algebras. J. Chungcheong Math. Soc. 22, 417–437 (2009)
Kaufmann, A.: Introduction a la Thiorie des Sous-Ensemble Flous, 1. Masson, Paris (1977)
Lee-kwang, H., Lee, K.-M.: Fuzzy hypergraph and fuzzy partition. IEEE Trans. Syst. Man Cybern. 25(1), 196–201 (1995)
Lung, R.I., Gasko, N., Suciu, M.A.: A hypergraph model for representing scientific output. Scientometrics 117(3), 1361–1379 (2018)
Mendel, J.M.: Uncertain Rule-based Fuzzy Logic Systems: Introduction and New Directions. Prentice-Hall, Upper Saddle River, New Jersey (2001)
Mordeson, J.N., Chang-Shyh, P.: Operations on fuzzy graphs. Inf. Sci. 79, 159–170 (1994)
Mordeson, J.N.: Fuzzy line graph. Pattern Recognit. Lett. 14, 381–384 (1993)
Mordeson, J.N., Nair, P.S.: Fuzzy Graphs and Fuzzy Hypergraphs, 2nd edn. Physica Verlag, Heidelberg (2001)
Mordeson, J.N., Yao, Y.Y.: Fuzzy cycles and fuzzy trees. J. Fuzzy Math. 10, 189–202 (2002)
Radhamani, C., Radhika, C.: Isomorphism on fuzzy hypergraphs. IOSR J. Math. 2(6), 24–31 (2012)
Radhika, C., Radhamani, C., Suresh, S.: Isomorphism properties on strong fuzzy hypergraphs. Int. J. Comput. Appl. 64(1)(2013)
Ramot, D., Milo, R., Friedman, M., Kandel, A.: Complex fuzzy sets. IEEE Trans. Fuzzy Syst. 10(2), 171–186 (2002)
Rosenfeld, A.: Fuzzy graphs. In: Zadeh, L.A., Fu, K.S., Shimura, M. (eds.) Fuzzy Sets and their Applications, pp. 77–95. Academic Press, New York (1975)
Samanta, S., Akram, M., Pal, M.: \(m\)-Step fuzzy competition graphs. J. Appl. Math. Comput. 47, 461–472 (2015)
Samanta, S., Pal, M.: Fuzzy \(k\)-competition graphs and \(p\)-competition fuzzy graphs. Fuzzy Inf. Eng. 5, 191–204 (2013)
Sarwar, M., Akram, M., Alshehri, N.O.: A new method to decision-making with fuzzy competition hypergraphs. Symmetry 10(9), 404 (2018). https://doi.org/10.3390/sym10090404
Sonntag, M., Teichert, H.M.: Competition hypergraphs. Discr. Appl. Math. 143, 324–329 (2004)
Sonntag, M., Teichert, H.M.: Competition hypergraphs of digraphs with certain properties II, Hamiltonicity. Discuss. Math. Graph Theory 28, 23–34 (2008)
Thirunavukarasu, P., Suresh, R., Viswanathan, K.K.: Energy of a complex fuzzy graph. Int. J. Math. Sci. Eng. Appl. 10(1), 243–248 (2016)
Yazdanbakhsh, O., Dick, S.: A systematic review of complex fuzzy sets and logic. Fuzzy Sets Syst. 338, 1–22 (2018)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)
Zadeh, L.A.: Similarity relations and fuzzy orderings. Inf. Sci. 3(2), 177–200 (1971)
Zadeh, L.A.: The concept of a linguistic and application to approximate reasoning-I. Inf. Sci. 8, 199–249 (1975)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Akram, M., Luqman, A. (2020). Fuzzy Hypergraphs. In: Fuzzy Hypergraphs and Related Extensions. Studies in Fuzziness and Soft Computing, vol 390. Springer, Singapore. https://doi.org/10.1007/978-981-15-2403-5_1
Download citation
DOI: https://doi.org/10.1007/978-981-15-2403-5_1
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-2402-8
Online ISBN: 978-981-15-2403-5
eBook Packages: EngineeringEngineering (R0)