Issue:Generalized real time multigraphs for communication networks: An intuitionistic fuzzy theoretical model

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Title of paper: Generalized real time multigraphs for communication networks: An intuitionistic fuzzy theoretical model Author(s): Siddhartha Sankar Biswas Department of Computer Engineering, Faculty of Engineering & Technology, Jamia Millia Islamia University, New Delhi – 110025, India ssbiswas1984@gmail.com Bashir Alam Department of Computer Engineering, Faculty of Engineering & Technology, Jamia Millia Islamia University, New Delhi – 110025, India M. N. Doja Department of Computer Engineering, Faculty of Engineering & Technology, Jamia Millia Islamia University, New Delhi – 110025, India Presented at: 17th International Conference on Intuitionistic Fuzzy Sets, 1–2 November 2013, Sofia, Bulgaria Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 19, 2013, Number 3, pages 90—98 Download:  PDF (378  Kb, File info) Abstract: This is sequel to our previous works on RT-multigraphs [21, 22] designed with intuitionistic fuzzy theory. In this paper, we introduce the notion of ‘Generalized Real Time Multigraph’ GRT-Multigraph) which is an improvement of the notion of RT multigraph. Any RT-multigraph is a special case of a GRT-multigraph. It is claimed that the model of GRTmultigraph will play a vital role in any network of communication system because of its high potential in considering real time data and information, and will open a new direction for rigorous research. Keywords: IFS; IFN; Multigraphs; RT-multigraphs; GRT-multigraphs; neighbor node; tbl; link status; LSV; LSC; tbn; rn; communicable node, CF, EC. AMS Classification: 05C85 References: Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 20, 1986, 87–96. Atanassov, K., Intuitionistic Fuzzy Sets: Theory and Applications, Springer, Heidelberg, 1999. Atanassov, K., On Intuitionistic Fuzzy Sets Theory, Springer, Berlin, 2012. Atanassov, K., Index matrix representation of the intuitionistic fuzzy graphs, Fifth Scientific Session of the Mathematical Foundations of Artificial Intelligence Seminar, Sofia, Oct. 5, 1994, Preprint MRL-MFAIS-10-94, 36–41. Atanassov, K. On index matrix interpretations of intuitionistic fuzzy graphs. Notes on Intuitionistic Fuzzy Sets, Vol. 8, 2002, No. 4, 73–78. Atanassov, K., Temporal intuitionistic fuzzy graphs, Notes on Intuitionistic Fuzzy Sets, Vol. 4, 1998, No. 4, 59–61. Atanassov, K., B. Papadopoulos, A. Syropoulos, An application of the theory of intuitionistic fuzzy multigraphs, Mathware & Soft Computing, Vol. 11, 2004, No. 1, 45–49. Balakrishnan, V. K., Graph Theory, McGraw–Hill; 1997. Bollobas, B., Modern Graph Theory, Springer; 2002. Li, D. F. A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problem, Computer and Mathematics with Applications, Vol. 60, 2010, 1557–1570. Diestel, R., Graph Theory, Springer, 2000. Dubois, D., H. Prade. Fuzzy Sets and Systems, Academic Press, New York, 1980. Harary, F., Graph Theory, Addison Wesley Publishing Company, 1995. Jenson, P., J. Barnes. Network Flow Programming, John Wiley and Sons, New York. 1980. Ivančo, J. Decompositions of multigraphs into parts with the same size, Discussiones Mathematicae Graph Theory, Vol. 30, 2010, No. 2, 335–347. Karunambigai, M. G., R. Parvathi, K. Atanassov, N. Palaniappan, An Intuitionistic Fuzzy Graph Method for Finding the Shortest Paths in Networks, Advances in Soft Computing, Vol. 42, 2007, 3–10. Meszka, M., Z. Skupien, Decomposition of a Complete Multigraph into Almost Arbitrary Paths, Discussiones Mathematicae Graph Theory, Vol. 32, 2012, No. 2, 357–372. Shannon, A., K. Atanassov, A First Step to A Theory of The Intuitionistic Fuzzy Graphs, Proceedings of 1st Workshop on Fuzzy Based Expert Systems (D. Lakov, Ed.), Sofia, Sept. 28-30, 1994, 59–61. Shannon A., K. Atanassov. On intuitionistic fuzzy multigraphs and their index matrix interpretations. Proceedings of 2nd International IEEE Conference on Intelligent Systems, 2004, Vol. 2, 440–443. Siddhartha Sankar Biswas, Basir Alam, M.N. Doja, A Theoretical Characterization of the Data Structure ‘Multigraphs’, Journal of Contemporary Applied Mathematics, Vol. 2, Dec. 2012, No. 2, 88–106. Siddhartha Sankar Biswas, Basir Alam, M. N. Doja, Real Time Multigraphs For Communication Networks: An Intuitionistic Fuzzy Mathematical Model, accepted for publication in Journal of Computer Science (to appear). Siddhartha Sankar Biswas, Basir Alam, M. N. Doja, Intuitionistic Fuzzy Real Time Multigraphs for Communication Networks: A Theoretical Model, Proceedings of 2013 AASRI Conference on Parallel and Distributed Computing Systems (DCS 2013), Singapore, © 2013 Published by Elsevier B.V. Selection and/or peer review under responsibility of American Applied Science Research Institute. Zadeh, L. A., Fuzzy Sets, Information and Control, Vol. 8, 1965, 338–353. Citations: The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.