Fuzzy Graph Coloring in Traffic Lights Problem

Subject Areas : Statistics

Yahya Talebi Rostami ¹ , Siyamak Firouzian ² , Ali Reza Moniri Hamzekolaee ³ , Mostafa Nouri Jouybari ⁴

1 - Associate Professor, Department of Mathematics, University of Mazandaran, Babolsar, Iran
2 - Department of Mathematics, Payame Noor University (PNU), Tehran, Iran
3 - Assistant Professor, Department of Mathematics, University of Mazandaran, Babolsar, Iran
4 - Department of Mathematics, Payame Noor University (PNU), Tehran, Iran

Received: 2019-03-25 Accepted : 2020-11-17 Published : 2021-02-19

Keywords: رنگ آمیزی فازی, مساله برنامه جدول زمانی, نظریه گراف, بهینه سازی,

Abstract :

Graph coloring is one of the issues that has been most noticed among combinatorial optimization issues. Many useful utility issues can be modeled as graph coloring issues. The general form of this application is to form a graph with nodes representing our favorite parts. The main problem of coloring the graph is the grouping of vertex graphs in small groups, so that no two heterogeneous vertices are in the same group. An important part of the application of graph coloring problem in management science is. The concept of traffic lights includes controlling the system of a traffic light so that a safe level of safety can be obtained. Modeling the problem of traffic lights has been proposed as a problem of assignment in combinatorial theory. This problem is also modeled as a graph coloring problem. In this paper, we have tried to model these problems in practical examples as the problem of staining the fuzzy graph and compare them with the proposed methods.

References:

 

[1] Ch. Eslahchi, B. N. Onagh, Vertex-strength of fuzzy graphs, International Journal of Mathematics and Mathematical Sciences, (2006), pages 1-9, ArticleID: 043614, DOI: 10.1155/ IJMMS/ 2006/ 43614

 

[2] A. Kishore, M. S. Sunitha, Chromatic number of fuzzy graphs, Annals of Fuzzy Mathematics and Informatics, 7(4), (2014) 543-551.

 

[3] A. Kaufmann, Introduction à la théorie des sous-ensembles Nous, 1 Eléments théoriques de base. Paris: Masson et Cie; 1976.

 

[4] J. N. Mordeson, M. J. Wierman, T. D. Clark, A. Pham, M. A. Redmond, Linear Models in the Mathematics of Uncertainty. Studies in Computational Intelligence, vol. 463, Springer, Berlin, 2013.

 

[5] S. Munoz, M. T. Ortuno, J. Ramirez, J. Yanez, Coloring fuzzy graphs, Omega, Elsevier 33(3), (2005) 211 – 221.

 

[6] A. Rosenfeld, Fuzzy graphs. In: Zadeh LA, Fu KS, Shimura M, editors. Fuzzy sets and their applications to cognitive and decision processes. New York: Academic Press; (1975), 77–95.

 

[7] S. Sovan, T. Pramanik, M. Pal, Fuzzy coloring of fuzzy graphs, Afrika Matematica, Volume 27(2), (2016) 37-50.

 

[8] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965) 338-353.

 

[9] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning, Information Sciences, 8(3) (1975) 199–249.