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Fuzzy Routing Protocol for D2D Communications Based on Probabilistic Normed Spaces

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Abstract

In this paper, a D2D multiple-metric routing protocol is proposed in the situation that the network infrastructures are ruined due to a possible natural disaster. To improve the stability and the shortness of the path, we use fuzzy mathematics and probabilistic normed spaces in such a way that the set of nodes is considered as a fuzzy set. This protocol operates in a distributed manner and at each stage independently finds the appropriate node. By introducing a stability indicator, we show that our method, while close to the shortest path, maintains durability.

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References

  1. Mach, P., Becvar, Z., & Vanek, T. (2015). In-band device-to-device communication in OFDMA cellular networks: A survey and challenges. IEEE Communications Surveys & Tutorials, 17(4), 1885–1922.

    Article  Google Scholar 

  2. Jameel, F., Hamid, Z., Jabeen, F., Zeadally, S., & Javed, M. A. (2018). A survey of device-to-device communications: Research issues and challenges. IEEE Communications Surveys & Tutorials, 20(3), 2133–2168.

    Article  Google Scholar 

  3. Rashed, S. K., Asvadi, R., Rajabi, S., Ghorashi, S. A., & Martini, M. G. (2020). Power allocation for D2D communications using max-min message-passing algorithm. IEEE Transactions on Vehicular Technology, 69(8), 8443–8458.

    Article  Google Scholar 

  4. Rajabi, S., Ghorashi, S. A., Shah-Mansouri, V., & Karami, H. (2017). Device-to-device communications using EMTR technique. IET Signal Processing, 12(3), 320–326.

    Article  Google Scholar 

  5. Bellman, R., Kalaba, R., & Zadeh, L. (1966). Abstraction and pattern classification. Journal of Mathematical Analysis and Applications, 13(1), 1–7.

    Article  MathSciNet  Google Scholar 

  6. Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management Science, 17(4), B-141.

    Article  MathSciNet  Google Scholar 

  7. Zadeh, L. A. (1977). Fuzzy sets and their application to pattern classification and clustering analysis. In: Classification and clustering (pp. 251–299). Elsevier

  8. Bezdek, J. C. (1973). Fuzzy mathematics in pattern classification. Ph.D. Dissertation, Applied Mathematics, Cornell University.

  9. Dunn, J. C. (1973). A fuzzy relative of the isodata process and its use in detecting compact well-separated clusters.

  10. Mamdani, E. H., & Assilian, S. (1975). An experiment in linguistic synthesis with a fuzzy logic controller. International Journal of Man-Machine Studies, 7(1), 1–13.

    Article  Google Scholar 

  11. Kosko, B. (1992). Neural networks and fuzzy systems: A dynamical systems approach to machine intelligence. (QA76), 76. E95 K86

  12. Ahvar, E., Pourmoslemi, A., Piran, M. J. (2011). Fear: A fuzzy-based energy-aware routing protocol for wireless sensor networks. arXiv preprint arXiv:1108.2777.

  13. Bělohlávek, R., Dauben, J. W., & Klir, G. J. (2017). Fuzzy Logic and Mathematics: A Historical Perspective. Oxford: Oxford University Press.

    Book  Google Scholar 

  14. Shaikh, F. S., & Wismüller, R. (2018). Routing in multi-hop cellular device-to-device (D2D) networks: A survey. IEEE Communications Surveys & Tutorials, 20(4), 2622–2657.

    Article  Google Scholar 

  15. Nunes, I. O., Celes, C., Nunes, I., de Melo, P. O. V., & Loureiro, A. A. (2018). Combining spatial and social awareness in D2D opportunistic routing. IEEE Communications Magazine, 56(1), 128–135.

    Article  Google Scholar 

  16. Othmen, S., Zarai, F., Belghith, A., & Kamoun, L. (2016). Anonymous and secure on-demand routing protocol for multi-hop cellular networks. In 2016 International Symposium on Networks, Computers and Communications (ISNCC) (pp. 1–6). IEEE.

  17. Casetti, C., Chiasserini, C. F., Pelle, L. C., Del Valle, C., Duan, Y., & Giaccone, P. (2015). “Content-centric routing in wi-fi direct multi-group networks,” In 2015 IEEE 16th international symposium on a world of wireless, mobile and multimedia networks (WoWMoM). IEEE, pp. 1–9.

  18. Kannan, G., Merchant, S. N., & Desai, U. B. (2007). “Cross layer routing for multihop cellular networks,” In 21st International Conference on Advanced Information Networking and Applications Workshops (AINAW’07), vol. 2. IEEE, pp. 165–170.

  19. Yuan, H., Guo, W., Jin, Y., Wang, S., & Ni, M. (2017). Interference-aware multi-hop path selection for device-to-device communications in a cellular interference environment. Iet Communications, 11(11), 1741–1750.

    Article  Google Scholar 

  20. Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338–353.

    Article  MathSciNet  Google Scholar 

  21. Cho, Y. J., Rassias, T. M., & Saadati, R. (2018). Fuzzy operator theory in mathematical analysis. Berlin: Springer.

    Book  Google Scholar 

  22. Klement, E. P., Mesiar, R., & Pap, E. (2013). Triangular norms (Vol. 8). Berlin: Springer.

    MATH  Google Scholar 

  23. Schweizer, B. (1961). Associative funcrions and statistical triangle inequalities. Publicationes Mathematicae Debrecen, 8, 169–186.

    MathSciNet  MATH  Google Scholar 

  24. Munir, M., Kalsoom, H., Ullah, K., Mahmood, T., & Chu, Y.-M. (2020). T-spherical fuzzy Einstein hybrid aggregation operators and their applications in multi-attribute decision making problems. Symmetry, 12(3), 365.

    Article  Google Scholar 

  25. Solanki, A., & Kumar, E. (2013). A novel technique for rule advancement in fuzzy expert system using Einstein sum.

  26. Wei, G., & Zhao, X. (2013). Induced hesitant interval-valued fuzzy Einstein aggregation operators and their application to multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 24(4), 789–803.

    Article  MathSciNet  Google Scholar 

  27. Zhao, X., & Wei, G. (2013). Some intuitionistic fuzzy Einstein hybrid aggregation operators and their application to multiple attribute decision making. Knowledge-Based Systems, 37, 472–479.

    Article  Google Scholar 

  28. Menger, K. (1942). Statistical metrics. Proceedings of the National Academy of Sciences of the United States of America, 28(12), 535.

    Article  MathSciNet  Google Scholar 

  29. Serstnev, A. (1963). The notion of random normed space. Doki Acad Nauk. Ussr., 149, 280–283.

    Google Scholar 

  30. Guillen, B. L., & Harikrishnan, P. (2014). Probabilistic normed spaces. London: Imperial College.

    Book  Google Scholar 

  31. Alsina, C., Schweizer, B., & Sklar, A. (1993). On the definition of a probabilistic normed space. Aequationes mathematicae, 46(1–2), 91–98.

    Article  MathSciNet  Google Scholar 

  32. Pourmoslemi, A., & Salimi, M. (2009). Probabilistic n-normed spaces, Dn-compact sets and Dn-bounded sets. Chaos, Solitons & Fractals, 42(5), 2729–2734.

    Article  MathSciNet  Google Scholar 

  33. Pourmoslemi, A., Ferrara, M., Pansera, B. A., & Salimi, M. (2020). Probabilistic norms on the homeomorphisms of a group. Soft Computing, 24, 7021–7028.

    Article  Google Scholar 

  34. Rajabi, S., Ghorashi, S., & Shah-Mansouri, V. (2018). Impact of connecting to the nth nearest node in dedicated device-to-device communications. Electronics Letters, 54(8), 535–537.

    Article  Google Scholar 

  35. Pourmoslemi, A, Rajabi, S., & Salimi, M. (2020). Selecting the best transmitter in wireless device-to-device communications using a fuzzy decision-making method. In International online conference on intelligent decision science (pp. 509–520). Springer.

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Authors and Affiliations

  1. Department of Mathematics, Payame Noor University, P.O. BOX 19395-3697, Tehran, Iran

    Alireza Pourmoslemi

  2. Department of Electrical Engineering, Hamedan University of Technology, Hamedan, 65155, Iran

    Siavash Rajabi

  3. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada

    Mehdi Salimi

  4. Institute of IR 4.0, The National University of Malaysia, 43600, UKM, Malaysia

    Ali Ahmadian

  5. Department of Mathematics, Near East University, TRNC, Nicosia, Mersin 10, Turkey

    Ali Ahmadian

  6. Department of Mathematics & Statistics, St. Francis Xavier University, Antigonish, NS, Canada

    Mehdi Salimi

Authors
  1. Alireza Pourmoslemi
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  2. Siavash Rajabi
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  3. Mehdi Salimi
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  4. Ali Ahmadian
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Correspondence to Ali Ahmadian.

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Pourmoslemi, A., Rajabi, S., Salimi, M. et al. Fuzzy Routing Protocol for D2D Communications Based on Probabilistic Normed Spaces. Wireless Pers Commun 122, 2505–2520 (2022). https://doi.org/10.1007/s11277-021-09009-7

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  • DOI: https://doi.org/10.1007/s11277-021-09009-7

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