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.
Similar content being viewed by others
References
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.
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.
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.
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.
Bellman, R., Kalaba, R., & Zadeh, L. (1966). Abstraction and pattern classification. Journal of Mathematical Analysis and Applications, 13(1), 1–7.
Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management Science, 17(4), B-141.
Zadeh, L. A. (1977). Fuzzy sets and their application to pattern classification and clustering analysis. In: Classification and clustering (pp. 251–299). Elsevier
Bezdek, J. C. (1973). Fuzzy mathematics in pattern classification. Ph.D. Dissertation, Applied Mathematics, Cornell University.
Dunn, J. C. (1973). A fuzzy relative of the isodata process and its use in detecting compact well-separated clusters.
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.
Kosko, B. (1992). Neural networks and fuzzy systems: A dynamical systems approach to machine intelligence. (QA76), 76. E95 K86
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.
Bělohlávek, R., Dauben, J. W., & Klir, G. J. (2017). Fuzzy Logic and Mathematics: A Historical Perspective. Oxford: Oxford University Press.
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.
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.
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.
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.
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.
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.
Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338–353.
Cho, Y. J., Rassias, T. M., & Saadati, R. (2018). Fuzzy operator theory in mathematical analysis. Berlin: Springer.
Klement, E. P., Mesiar, R., & Pap, E. (2013). Triangular norms (Vol. 8). Berlin: Springer.
Schweizer, B. (1961). Associative funcrions and statistical triangle inequalities. Publicationes Mathematicae Debrecen, 8, 169–186.
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.
Solanki, A., & Kumar, E. (2013). A novel technique for rule advancement in fuzzy expert system using Einstein sum.
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.
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.
Menger, K. (1942). Statistical metrics. Proceedings of the National Academy of Sciences of the United States of America, 28(12), 535.
Serstnev, A. (1963). The notion of random normed space. Doki Acad Nauk. Ussr., 149, 280–283.
Guillen, B. L., & Harikrishnan, P. (2014). Probabilistic normed spaces. London: Imperial College.
Alsina, C., Schweizer, B., & Sklar, A. (1993). On the definition of a probabilistic normed space. Aequationes mathematicae, 46(1–2), 91–98.
Pourmoslemi, A., & Salimi, M. (2009). Probabilistic n-normed spaces, Dn-compact sets and Dn-bounded sets. Chaos, Solitons & Fractals, 42(5), 2729–2734.
Pourmoslemi, A., Ferrara, M., Pansera, B. A., & Salimi, M. (2020). Probabilistic norms on the homeomorphisms of a group. Soft Computing, 24, 7021–7028.
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.
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
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
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11277-021-09009-7