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M-AHP and GRA Based a Hybrid Double-Layered Technique for Selecting the Optimal and Best Relay in Cooperative CR Networks

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Abstract

When it comes to cooperative transmission in wireless communication, relay-aided transmission is the new benchmark. However, the selection of relays is a very critical issue; hence, nowadays, this problem emerges as a demanding topic in research. The optimum relay selection framework is essential to achieve reliable transmission, maintaining QoS of the primary transmission in the cognitive radio system. In this paper, the authors propose a novel hybrid relay selection framework integrating two different MCDM, i.e., multiple criteria decision-making techniques, specifically M-AHP (multiple analytical hierarchy process) and GRA (grey relational analysis). Here, criteria weights are determined using M-AHP process in the first layer, which considers multiple scenarios that are absent in Saaty’s AHP. To find out the best available relay or carrier, GRA is applied in the second layer here as it works efficiently on uncertainty problems containing incomplete information and discrete data. To find out the best relays, numerical examples, simulation studies with process flow, all are conducted in this work.

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Abbreviations

\(P_{PT}\) :

Transmission power of PT

\(P_{ST}\) :

Transmission power of ST

\(r_{PT}\) :

Data rate of PT

\(r_{ST}\) :

Data rate of ST

\(SR_{i}\) :

‘i’ th Secondary Relay

K :

Total number of relay nodes

\(\Re\) :

Set of Secondary Relays \(\Re = \left\{ {\left. {SR_{i} } \right| \, i = 1, \, 2,{ 3 }.... \, K} \right\}\)

\(c_{u,v}\) :

Channel impulse response

\(\alpha_{{{\text{u}},v}}\) :

Instantaneous channel gain between nodes u and v

\(\Phi_{D}\) :

Decoding Set \(\Phi_{D} \, = \, \left\{ {\varphi \, \left| { \, \varphi \, \in \, \phi \, \cup \, \varphi_{{\text{k }}} {\text{ , k}} = { 1, 2 }...{, 2}^{{\text{K}}} - 1} \right.} \right\}\)

\(\gamma\) :

Path loss coefficient

\(d_{{{\text{u}},{\text{v}}}}\) :

Path length connecting elements u & v

\({\text{g}}_{{_{{\text{u, v}}} }}\) :

Fading coefficient with zero-mean

\(X_{{\text{S}}}\) :

Secondary data

\(\varphi_{{\text{K}}}\) :

Non zero sub-group of ‘K’ relays

\(\phi\) :

Null set

\(\mathop \beta \nolimits_{SRj}\) :

Reliability

\(\lambda_{\max }\) :

Eigenvalue

\(\Omega_{{\text{S}}}\) :

Successful transmission rate of node SRj

\(\Omega_{F}\) :

Failure transmission rate of SRj

\(\overline{\Gamma }_{{\text{S}}}\) :

Mean amount of fruitful communications are performed by node SRj

\(w_{{{\text{ahp}}_{{{\text{intermediate}}}} }}\) :

Local criteria weights

\(w_{{{\text{ahp}}_{{{\text{global}}}} }}\) :

Global weights of alternatives

\(a_{j}^{*} (i)\) :

Normalized data set for larger-is-better or smaller-is-better

\(\zeta_{0j} (i)\) :

Grey relational coefficient

\(\vartheta_{0j}\) :

Degree of the grey equation coefficient

References

  1. I.F. Akyildiz, X. Wang, W. Wang, Wireless mesh networks: a survey. Comput. Netw. 47(4), 445–487 (2005)

    Article  MATH  Google Scholar 

  2. I.F. Akyildiz, W.Y. Lee, K.R. Chowdhury, CRAHNs: cognitive radio ad hoc networks. Ad Hoc Netw. 7(5), 810–836 (2009)

    Article  Google Scholar 

  3. X. Gao, G. Wu, T. Miki, End-to-end QoS provisioning in mobile heterogeneous networks. IEEE Wirel. Commun. 11(3), 24–34 (2004)

    Article  Google Scholar 

  4. FCC, ET Docket No 03–322 Notice of Proposed Rule Making and Order, Dec (2003)

  5. J.S. Banerjee, A. Chakraborty, Fundamentals of Software Defined Radio and Cooperative Spectrum Sensing: A Step Ahead of Cognitive Radio Networks, in Handbook of Research on Software-Defined and Cognitive Radio Technologies for Dynamic Spectrum Management. ed. by N. Kaabouch, W. Hu (IGI Global, USA, 2015), pp.499–543

    Chapter  Google Scholar 

  6. J.S. Banerjee, A. Chakraborty, Modeling of Software Defined Radio Architecture & Cognitive Radio, the Next Generation Dynamic and Smart Spectrum Access Technology, in Cognitive Radio Sensor Networks: Applications, Architectures, and Challenges. ed. by M.H. Rehmani, Y. Faheem (IGI Global, USA, 2014), pp.127–158

    Chapter  Google Scholar 

  7. J. S. Banerjee, A. Chakraborty, and K. Karmakar, Architecture of Cognitive Radio Networks, In: N. Meghanathan & Y.B.Reddy (Ed.), Cognitive Radio Technology Applications for Wireless and Mobile Ad Hoc Networks, IGI Global, USA, 125–152, (2013)

  8. A. Chakraborty, J.S. Banerjee, An advance Q learning (AQL) approach for path planning and obstacle avoidance of a mobile robot. Int. J. Intell. Mechatron. Robot. (IJIMR) 3(1), 53–73 (2013)

    Google Scholar 

  9. J.S. Banerjee, K. Karmakar, A comparative Study on Cognitive Radio Implementation Issues. Int. J. Comput. Appl. 45(15), 44–51 (2012)

    Google Scholar 

  10. A. Bletsas, A. Khisti, D.P. Reed, A. Lippman, A simple cooperative diversity method based on network path selection. IEEE J. Sel. Areas Commun. 24(3), 659–672 (2006)

    Article  Google Scholar 

  11. N. Zhang, N. Lu, R. Lu, J. W. Mark, & X. Shen, Energy-efficient and trust-aware cooperation in cognitive radio networks. In 2012 IEEE international conference on communications (ICC) (pp. 1763–1767). IEEE, (2012)

  12. E. Beres, R. Adve, Selection cooperation in multi-source cooperative networks. IEEE Trans. Wireless Commun. 7(1), 118–127 (2008)

    Article  Google Scholar 

  13. O. Simeone, Y. Bar-Ness, U. Spagnolini, Stable throughput of cognitive radios with and without relaying capability. IEEE Trans. Commun. 55(12), 2351–2360 (2007)

    Article  Google Scholar 

  14. R. Lu, X. Li, X. Liang, X. Shen, X. Lin, GRS: The green, reliability, and security of emerging machine to machine communications. IEEE Commun. Mag. 49(4), 28–35 (2011)

    Article  Google Scholar 

  15. S. Marti, T. J. Giuli, K. Lai, & M. Baker, Mitigating routing misbehavior in mobile ad hoc networks. In Proceedings of the 6th annual international conference on Mobile computing and networking, pp. 255–265 (2000)

  16. A. Urpi, M. Bonuccelli, & S. Giordano, Modelling cooperation in mobile ad hoc networks: a formal description of selfishness. In WiOpt'03: modeling and optimization in mobile, ad hoc and wireless networks, pp. 10 (2003)

  17. V. Srinivasan, P. Nuggehalli, C. F. Chiasserini, and R. R. Rao, Cooperation in wireless ad hoc networks, In: Proceedings of the IEEE Infocom’03, (2003)

  18. Y. Zou, Y.D. Yao, B. Zheng, Diversity-multiplexing tradeoff in selective cooperation for cognitive radio. IEEE Trans. Commun. 60(9), 2467–2481 (2012)

    Article  Google Scholar 

  19. B. Razeghi, M. Hatamian, A. Naghizadeh, S. Sabeti, & G. A. Hodtani, A novel relay selection scheme for multi-user cooperation communications using fuzzy logic. In 2015 IEEE 12th International Conference on Networking, Sensing and Control (pp. 241–246). IEEE, (2015)

  20. J. S. Banerjee, A. Chakraborty, and A. Chattopadhyay, Fuzzy based relay selection for secondary transmission in cooperative cognitive radio networks. In Proceedings of Advances in Optical Science and Engineering (pp. 279–287), (2017)

  21. J.S. Banerjee, A. Chakraborty, A. Chattopadhyay, Reliable best-relay selection for secondary transmission in co-operation based cognitive radio systems: a multi-criteria approach. J. Mech. Continua Math. Sci 13(2), 24–42 (2018)

    Google Scholar 

  22. J. S. Banerjee, A. Chakraborty, and A. Chattopadhyay, Relay node selection using analytical hierarchy process (AHP) for secondary transmission in multi-user cooperative cognitive radio systems. In Advances in Electronics, Communication and Computing (pp. 745–754). Springer, Singapore, (2018)

  23. S. A. Alvi, R. Hussain, A. Shakeel, M. A. Javed, Q. U. Hasan, B. M. Lee, & S. A. Malik, QoS-oriented optimal relay selection in cognitive radio networks. Wirel. Commun. Mob. Comput. (2021)

  24. K. Ho-Van, & T. Do-Dac, Relay selection for security improvement in cognitive radio networks with energy harvesting. Wirel. Commun. Mob. Comput. (2021)

  25. V. Aswathi, A.V. Babu, Performance analysis of NOMA-based underlay cognitive radio networks with partial<? brk?> relay selection. IEEE Trans. Veh. Technol. 70(5), 4615–4630 (2021)

    Article  Google Scholar 

  26. O.A. Amodu, M. Othman, N.K. Noordin, I. Ahmad, Outage minimization of energy harvesting-based relay-assisted random underlay cognitive radio networks with interference cancellation. IEEE Access 9, 109432–109446 (2021)

    Article  Google Scholar 

  27. Z. Yan, H.M. Kong, W. Wang, H.L. Liu, X. Shen, Reliability Benefit of Location-based Relay Selection for Cognitive Relay Networks. IEEE Internet Things J. 9(3), 2319–2329 (2021)

    Article  Google Scholar 

  28. J.S. Banerjee, A. Chakraborty, A. Chattopadhyay, A cooperative strategy for trustworthy relay selection in cr network: a game-theoretic solution. Wirel. Pers. Commun. 122(1), 41–67 (2022)

    Article  Google Scholar 

  29. J. Banerjee, S. Maiti, S. Chakraborty, S. Dutta, A. Chakraborty, & J. S. Banerjee, Impact of machine learning in various network security applications. In 2019 3rd International Conference on Computing Methodologies and Communication (ICCMC) (pp. 276–281). IEEE, (2019)

  30. K. Das, & J. S. Banerjee, Cognitive Radio-Enabled Internet of Things (CR-IoT): An Integrated Approach towards Smarter World. In Applications of Machine Intelligence in Engineering (pp. 541–555). CRC Press, (2022)

  31. J. K. Mandal, S. Misra, Banerjee, J. S. Banerjee, & S. Nayak, (Eds.). Applications of Machine intelligence in Engineering: Proceedings of 2nd Global Conference on Artificial Intelligence and Applications (GCAIA, 2021), September 8–10, 2021, Jaipur, India. CRC Press, (2022)

  32. K. Das, & J. S. Banerjee, Green IoT for Intelligent Cyber-Physical Systems in Industry 4.0: A Review of Enabling Technologies, and Solutions. In Applications of Machine Intelligence in Engineering (pp. 463–478). CRC Press, (2022)

  33. K. Geng, Q. Gao, L. Fei, H. **ong, Relay selection in cooperative communication systems over continuous time-varying fading channel. Chin. J. Aeronaut. 30(1), 391–398 (2017)

    Article  Google Scholar 

  34. K. Ho-Van, Exact outage probability analysis of proactive relay selection in cognitive radio networks with MRC receivers. J. Commun. Netw. 18(3), 288–298 (2016)

    Article  Google Scholar 

  35. X. Zhang, K. An, B. Zhang, Z. Chen, Y. Yan, D. Guo, Vickrey auction-based secondary relay selection in cognitive hybrid satellite-terrestrial overlay networks with non-orthogonal multiple access. IEEE Wirel. Commun. Lett. 9(5), 628–632 (2020)

    Article  Google Scholar 

  36. S. Silva, M. Ardakani, C. Tellambura, Interference suppression and energy efficiency improvement with massive mimo and relay selection in cognitive two-way relay networks. IEEE Trans. Green Commun. Netw. 4(2), 326–339 (2020)

    Article  Google Scholar 

  37. M.K. Simon, M.S. Alouini, Digital Communication Over Fading Channels (Wiley, USA, 2005)

    Google Scholar 

  38. S. Kandukuri, S. Boyd, Optimal power control in interference-limited fading wireless channels with outage-probability specifications. IEEE Trans. Wirel. Commun. 1(1), 46–55 (2002)

    Article  Google Scholar 

  39. Q. Zhang, J. Jia, J. Zhang, Cooperative relay to improve diversity in cognitive radio networks. IEEE Commun. Mag. 47(2), 111–117 (2009)

    Article  MathSciNet  Google Scholar 

  40. G. Zhao, C. Yang, G.Y. Li, D. Li, A.C. Soong, Power and channel allocation for cooperative relay in cognitive radio networks. IEEE J. Sel. Top. Signal Proc. 5(1), 151–159 (2010)

    Article  Google Scholar 

  41. H. Yu, W. Tang, & S. Li, Joint optimal sensing and power allocation for cooperative relay in cognitive radio networks. In Proceedings of the 2012 IEEE International Conference on Communications (ICC) (pp. 1635–1640). IEEE, (2012)

  42. J. Jia, & J. Zhang, and Q. Zhang, Cooperative relay for cognitive radio networks. In Proceedings of the IEEE INFOCOM 2009 (pp. 2304–2312). IEEE, (2009)

  43. W. Jaafar, W. Ajib, & D. Haccoun, A novel relay-aided transmission scheme in cognitive radio networks. In Proceedings of the 2011 IEEE Global Telecommunications Conference-GLOBECOM 2011 (pp. 1–6). IEEE, (2011)

  44. W. Jaafar, W. Ajib, & D. Haccoun, Opportunistic adaptive relaying in cognitive radio networks. In Proceedings of the 2012 IEEE International Conference on Communications (ICC) (pp. 1811–1815). IEEE, (2012)

  45. W. Jaafar, W. Ajib, & D. Haccoun, Incremental relaying transmissions with relay selection in cognitive radio networks. In Proceedings of the 2012 IEEE Global Communications Conference (GLOBECOM) (pp. 1230–1235). IEEE, (2012)

  46. T. Do, B.L. Mark, Joint spatial–temporal spectrum sensing for cognitive radio networks. IEEE Trans. Veh. Technol. 59(7), 3480–3490 (2010)

    Article  Google Scholar 

  47. H. Luo, Z. Zhang, & G. Yu, Cognitive cooperative relaying. In Proceedings of the 2008 11th IEEE Singapore International Conference on Communication Systems (pp. 1499–1503). IEEE, (2008)

  48. T. **g, S. Zhu, H. Li, X. **ng, X. Cheng, Y. Huo, T. Znati, Cooperative relay selection in cognitive radio networks. IEEE Trans. Veh. Technol. 64(5), 1872–1881 (2014)

    Article  Google Scholar 

  49. I. Krikidis, T. Charalambous, J.S. Thompson, Buffer-aided relay selection for cooperative diversity systems without delay constraints. IEEE Trans. Wirel. Commun. 11(5), 1957–1967 (2012)

    Article  Google Scholar 

  50. A. Alsharoa, F. Bader, M.S. Alouini, Relay selection and resource allocation for two-way DF-AF cognitive radio networks. IEEE Wirel. Commun. Lett 2(4), 427–430 (2013)

    Article  Google Scholar 

  51. S. Zhang, V.K. Lau, Multi-relay selection design and analysis for multi-stream cooperative communications. IEEE Trans. Wirel. Commun. 10(4), 1082–1089 (2011)

    Article  Google Scholar 

  52. L. Song, Relay selection for two-way relaying with amplify-and-forward protocols. IEEE Trans. Veh. Technol. 60(4), 1954–1959 (2011)

    Article  Google Scholar 

  53. Y. Zou, J. Zhu, B. Zheng, Y.D. Yao, An adaptive cooperation diversity scheme with best-relay selection in cognitive radio networks. IEEE Trans. Signal Process. 58(10), 5438–5445 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  54. Y. Zou, J. Zhu, B. Zheng, S. Tang, & Y. D. Yao, A cognitive transmission scheme with the best relay selection in cognitive radio networks. In Proceedings of the 2010 IEEE Global Telecommunications Conference GLOBECOM 2010 (pp. 1–5). IEEE, (2010)

  55. Y. Ma, M. R. Kibria, & A. Jamalipour, Optimized routing framework for intermittently connected mobile ad hoc networks. In Proceedings of the 2008 IEEE International Conference on Communications (pp. 3171–3175). IEEE, (2008)

  56. B. Kim, J. Cho, S. Jeon, B. Lee, An AHP-based flexible relay node selection scheme for WBANs. Wirel. Pers. Commun. 89(2), 501–520 (2016)

    Article  Google Scholar 

  57. J.S. Banerjee, A. Chakraborty, A. Chattopadhyay, A decision model for selecting best reliable relay queue for cooperative relaying in cooperative cognitive radio networks: the extent analysis based fuzzy AHP solution. Wireless Netw. 27(4), 2909–2930 (2021)

    Article  Google Scholar 

  58. S. Guhathakurata, S. Saha, S. Kundu, A. Chakraborty, & J. S. Banerjee, South Asian Countries are less fatal concerning COVID-19: a fact-finding procedure integrating machine learning & multiple criteria decision-making (MCDM) technique”. Journal of The Institution of Engineers (India): Series B, 1–15, (2021)

  59. S. Guhathakurata, S. Saha, S. Kundu, A. Chakraborty, & J. S. Banerjee, South Asian countries are less fatal concerning COVID-19: a hybrid approach using machine learning and M-AHP. In: Computational Intelligence Techniques for Combating COVID-19, 1, (2021)

  60. O. Saha, A. Chakraborty, & J. S. Banerjee, A decision framework of IT-based stream selection using analytical hierarchy process (AHP) for admission in technical institutions. In Proceedings of 2017 4th International Conference on Opto-Electronics and Applied Optics (Optronix), (pp. 1–6), (2017)

  61. O. Saha, A. Chakraborty, & J. S. Banerjee, A fuzzy AHP approach to IT-based stream selection for admission in technical institutions in India. In Proceedings of Emerging Technologies in Data Mining and Information Security, (pp. 847–858), (2019)

  62. S. Paul, A. Chakraborty, & J. S. Banerjee, A fuzzy AHP-based relay node selection protocol for wireless body area networks (WBAN). In Proceedings of 2017 4th International Conference on Opto-Electronics and Applied Optics (Optronix), (pp. 1–6), (2017)

  63. S. Paul, A. Chakraborty, & J. S. Banerjee, The extent analysis based fuzzy AHP approach for relay selection in WBAN. In Proceedings of Cognitive Informatics and Soft Computing, (pp. 331–341), (2019)

  64. J. Kim, J. Lee, Opportunistic wireless network coding with relay node selection. EURASIP J. Wirel. Commun. Netw. 2011(1), 196 (2011)

    Article  Google Scholar 

  65. S. M. Elrabiei, & M. H. Habaebi, Energy efficient cooperative communication in single frequency networks. In Proceedings of the 21st Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (pp. 1719–1724). IEEE, (2010)

  66. N. Tuah, & M. Ismail, Extending lifetime of heterogenous wireless sensor network using relay node selection. In Proceedings of the 2013 International Conference of Information and Communication Technology (ICoICT) (pp. 17–21). IEEE, (2013)

  67. S. Biswas, L.K. Sharma, R. Ranjan, S. Saha, A. Chakraborty, J.S. Banerjee, Smart farming & water saving based intelligent irrigation system implementation using IoT (Recent Trends in Computational Intelligence Enabled Research, Elsevier, 2021), pp.339–354

    Google Scholar 

  68. R. Roy, S. Dutta, S. Biswas, & J. S. Banerjee, Android Things: A Comprehensive Solution from Things to Smart Display and Speaker. In Proceedings of International Conference on IoT Inclusive Life (ICIIL 2019), NITTTR Chandigarh, India (pp. 339–352), (2020).

  69. I. Pandey, H.S. Dutta, & J. S. Banerjee, WBAN: A Smart Approach to Next Generation e-healthcare System. In 2019 3rd International Conference on Computing Methodologies and Communication (ICCMC) (pp. 344–349). IEEE, (2019)

  70. D. Das, I. Pandey, A. Chakraborty, J.S. Banerjee, Analysis of implementation factors of 3D printer: the key enabling technology for making prototypes of the engineering design and manufacturing. Int. J. Comput. Appl. 1, 8–14 (2017)

    Google Scholar 

  71. D. Das, I. Pandey, & J. S. Banerjee, An in-depth Study of Implementation Issues of 3D Printer. In: Proc. MICRO 2016 Conference on Microelectronics, Circuits and Systems, pp. 45–49, (2016)

  72. J. S. Banerjee, D. Goswami, & S. Nandi, OPNET: a new paradigm for simulation of advanced communication systems. In Proceedings of International Conference on Contemporary Challenges in Management, Technology & Social Sciences, SEMS (pp. 319–328), (2014)

  73. M. de Graaf, Energy efficient networking via dynamic relay node selection in wireless networks. Ad Hoc Netw. 11(3), 1193–1201 (2013)

    Article  Google Scholar 

  74. P. Rajpoot, P. Dwivedi, Multiple parameter based energy balanced and optimized clustering for WSN to enhance the Lifetime using MADM Approaches. Wirel. Pers. Commun. 106(2), 829–877 (2019)

    Article  Google Scholar 

  75. A. Ehyaie, M. Hashemi, & P. Khadivi, Using relay network to increase life time in wireless body area sensor networks. In Proceedings of the 2009 IEEE International Symposium on a World of Wireless, Mobile and Multimedia Networks & Workshops (pp. 1–6). IEEE, (2009)

  76. J. Elias, & A. Mehaoua, Energy-aware topology design for wireless body area networks. In Proceedings of the 2012 IEEE international conference on communications (ICC) (pp. 3409–3410). IEEE, (2012)

  77. C.S. Lin, P.J. Chuang, Energy-efficient two-hop extension protocol for wireless body area networks. IET Wirel. Sens. Syst. 3(1), 37–56 (2013)

    Article  Google Scholar 

  78. J.S. Banerjee, A. Chakraborty, A. Chattopadhyay, A novel best relay selection protocol for cooperative cognitive radio systems using fuzzy AHP. J. Mech. Continua Math. Sci 13(2), 72–87 (2018)

    Google Scholar 

  79. A. Chakraborty, J.S. Banerjee, A. Chattopadhyay, Non-uniform quantized data fusion rule for data rate saving and reducing control channel overhead for cooperative spectrum sensing in cognitive radio networks”. Wirel. Pers. Commun. 104(2), 837–851 (2019)

    Article  Google Scholar 

  80. A. Chakraborty, J. S. Banerjee, and A. Chattopadhyay, Non-uniform quantized data fusion rule alleviating control channel overhead for cooperative spectrum sensing in cognitive radio networks. In 2017 IEEE 7th International Advance Computing Conference (IACC) (pp. 210–215). IEEE, (2017)

  81. A. Chakraborty, J.S. Banerjee, A. Chattopadhyay, Malicious node restricted quantized data fusion scheme for trustworthy spectrum sensing in cognitive radio networks. J. Mech. Contin. Math. Sci. 15(1), 39–56 (2020)

    Google Scholar 

  82. Y. Han, A. Pandharipande, S.H. Ting, Cooperative decode-and-forward relaying for secondary spectrum access. IEEE Trans. Wirel. Commun. 8(10), 4945–4950 (2009)

    Article  Google Scholar 

  83. S.S. Ikki, M.H. Ahmed, Performance analysis of adaptive decode-and-forward cooperative diversity networks with best-relay selection. IEEE Trans. Commun. 58(1), 68–72 (2010)

    Article  Google Scholar 

  84. T.L. Saaty, How to make a decision: the analytic hierarchy process. Eur. J. Oper. Res. 48(1), 9–26 (1990)

    Article  MATH  Google Scholar 

  85. T.L. Saaty, Decision making—the analytic hierarchy and network processes (AHP/ANP). J. Syst. Sci. Syst. Eng. 13(1), 1–35 (2004)

    Article  Google Scholar 

  86. C.I. Hsu, Y.H. Wen, Application of grey theory and multiobjective programming towards airline network design. Eur. J. Oper. Res. 127(1), 44–68 (2000)

    Article  MATH  Google Scholar 

  87. D. Julong, Introduction to grey system theory. J. Grey Syst. 1(1), 1–24 (1989)

    MathSciNet  MATH  Google Scholar 

  88. D. Ju-Long, Control problems of grey systems. Syst. Control Lett. 1(5), 288–294 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  89. M. Lahby, & A. Adib, Network selection mechanism by using M-AHP/GRA for heterogeneous networks. In 6th Joint IFIP Wireless and Mobile Networking Conference (WMNC) (pp. 1–6). IEEE, (2013, April)

  90. C.C. Yang, B.S. Chen, Supplier selection using combined analytical hierarchy process and grey relational analysis. J. Manuf. Technol. Manag. 17(7), 926–941 (2006)

    Article  Google Scholar 

  91. P. Holecek, J. Talašová, A free software tool implementing the fuzzy AHP method. In Proceedings of the 34th international conference on mathematical methods in economics 2016, Liberec, Czech Republic, 6–9 September 2016, pp. 266–271 (2016) (ISBN 978-80-7494-296-9)

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  1. Department of Electronics & Communication Engineering, Bengal Institute of Technology, Kolkata, 700150, India

    Jyoti Sekhar Banerjee & Arpita Chakraborty

  2. Department of Electronics & Communication Engineering, University of Engineering & Management, Kolkata, 700156, India

    Abir Chattopadhyay

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Banerjee, J.S., Chakraborty, A. & Chattopadhyay, A. M-AHP and GRA Based a Hybrid Double-Layered Technique for Selecting the Optimal and Best Relay in Cooperative CR Networks. J. Inst. Eng. India Ser. B 103, 1995–2011 (2022). https://doi.org/10.1007/s40031-022-00786-8

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