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AIMS Mathematics

2022, Volume 7, Issue 3: 4735-4766. doi: 10.3934/math.2022263
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Research article

Pythagorean Cubic fuzzy Hamacher aggregation operators and their application in green supply selection problem

  • 1.
    Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, KP, Pakistan
  • 2.
    Deanship of Combined First Year Umm Al-Qura University, Makkah, P.O. Box 715, Saudi Arabia
  • 3.
    School of Mathematics and Information, Neijiang Normal University, Neijiang, Sichuan, China
  • Received: 15 August 2021 Revised: 17 November 2021 Accepted: 25 November 2021 Published: 24 December 2021

  • MSC : 03E72, 47S40

  • The green chain supplier selection process plays a major role in the environmental decision for the efficient and effective supply chain management. Therefore, the aim of this paper is to develop a mechanism for decision making on green chain supplier problem. First, we define the Hamacher operational law for Pythagorean cubic fuzzy numbers (PCFNs) and study their fundamental properties. Based on the Hamacher operation law of PCFNs, we defined Pythagorean cubic fuzzy aggregation operators by using Hamacher t-norm and t-conorm. Further, we develop a series of Pythagorean cubic fuzzy Hamacher weighted averaging (PCFHWA), Pythagorean cubic fuzzy Hamacher order weighted averaging (PCFHOWA) Pythagorean Cubic fuzzy Hamacher hybrid averaging (PCFHHA), Pythagorean Cubic fuzzy Hamacher weighted Geometric (PCFHWG), Pythagorean Cubic fuzzy Hamacher order weighted Geometric (PCFHOWG), and Pythagorean Cubic fuzzy Hamacher hybrid geometric (PCFHHA) operators. Furthermore, we apply these aggregation operators of Pythagorean Cubic fuzzy numbers to the decision making problem for green supplier selection. We construct an algorithm for the group decision making by using aggregation operators and score function. The proposed decision making method applies to green chain supplier selection problem and find the best green supplier for green supply chain management. The proposed method compared with other group decision techniques under Pythagorean cubic fuzzy information. From the comparison and sensitivity analysis, we concluded that our proposed method is more generalized and effective method.

    Citation: Saleem Abdullah, Muhammad Qiyas, Muhammad Naeem, Mamona, Yi Liu. Pythagorean Cubic fuzzy Hamacher aggregation operators and their application in green supply selection problem[J]. AIMS Mathematics, 2022, 7(3): 4735-4766. doi: 10.3934/math.2022263

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  • The green chain supplier selection process plays a major role in the environmental decision for the efficient and effective supply chain management. Therefore, the aim of this paper is to develop a mechanism for decision making on green chain supplier problem. First, we define the Hamacher operational law for Pythagorean cubic fuzzy numbers (PCFNs) and study their fundamental properties. Based on the Hamacher operation law of PCFNs, we defined Pythagorean cubic fuzzy aggregation operators by using Hamacher t-norm and t-conorm. Further, we develop a series of Pythagorean cubic fuzzy Hamacher weighted averaging (PCFHWA), Pythagorean cubic fuzzy Hamacher order weighted averaging (PCFHOWA) Pythagorean Cubic fuzzy Hamacher hybrid averaging (PCFHHA), Pythagorean Cubic fuzzy Hamacher weighted Geometric (PCFHWG), Pythagorean Cubic fuzzy Hamacher order weighted Geometric (PCFHOWG), and Pythagorean Cubic fuzzy Hamacher hybrid geometric (PCFHHA) operators. Furthermore, we apply these aggregation operators of Pythagorean Cubic fuzzy numbers to the decision making problem for green supplier selection. We construct an algorithm for the group decision making by using aggregation operators and score function. The proposed decision making method applies to green chain supplier selection problem and find the best green supplier for green supply chain management. The proposed method compared with other group decision techniques under Pythagorean cubic fuzzy information. From the comparison and sensitivity analysis, we concluded that our proposed method is more generalized and effective method.


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    [1] K. T. Atanassov, More on intuitionistic fuzzy sets, Fuzzy Set. Syst., 33 (1989), 37–45. https://doi.org/10.1016/0165-0114(89)90215-7 doi: 10.1016/0165-0114(89)90215-7
    [2] S. G. Azevedo, C. Helena Carvalho, V. C. Machado, The influence of green practices on supply chain performance: A case study approach, Transport. Res. E-Log., 47 (2011), 850–871.
    [3] P. Ahi, C. Searcy, A comparative literature analysis of definitions for green and sustainable supply chain management, J. Clean. Prod., 52 (2013), 329–341. https://doi.org/10.1016/j.jclepro.2013.02.018 doi: 10.1016/j.jclepro.2013.02.018
    [4] H. Ala-Harja, P. Helo, Reprint of green supply chain decisions–Case-based performance analysis from the food industry, Transport. Res. Part E-Log., 74 (2015), 11–21.
    [5] S. Barari, G, Agarwal, W. J.(Chris), Zhang, B. Mahanty, M. K. Tiwari, A decision framework for the analysis of green supply chain contracts: An evolutionary game approach, Expert Syst. Appl., 39 (2012), 2965–2976. https://doi.org/10.1016/j.eswa.2011.08.158 doi: 10.1016/j.eswa.2011.08.158
    [6] S. M. Chen, C. H. Chang, Fuzzy multi-attribute decision making based on transformation techniques of intuitionistic fuzzy values and intuitionistic fuzzy geometric averaging operators. Inform. Sciences, 352 (2016), 133–149. https://doi.org/10.1016/j.ins.2016.02.049 doi: 10.1016/j.ins.2016.02.049
    [7] P. Centobelli, R. Cerchione, E. Esposito, Pursuing supply chain sustainable development goals through the adoption of green practices and enabling technologies: A cross-country analysis of LSPs, Technol. Forecast. Soc., 153 (2020), 119920. https://doi.org/10.1016/j.techfore.2020.119920 doi: 10.1016/j.techfore.2020.119920
    [8] F. Chiclana, F. Herrera, E. H. Viedma, The ordered weighted geometric operator: Properties and application, In: Proc of 8th Int Conf on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Madrid, (2000), 985–991.
    [9] H. Deng, Multicriteria analysis with fuzzy pairwise comparison, Int. J. Approx. Reason., 21 (1999), 215–231.
    [10] A. Diabat, K. Govindan, An analysis of the drivers affecting the implementation of green supply chain management, Resour. Conserv. Recy., 55 (2011), 659–667. https://doi.org/10.1016/j.resconrec.2010.12.002 doi: 10.1016/j.resconrec.2010.12.002
    [11] M. Dwivedy, R. K. Mittal, Willingness of residents to participate in e-waste recycling in India. Environ. Dev., 6 (2013), 48–68. https://doi.org/10.1016/S0026-0657(13)70237-6 doi: 10.1016/S0026-0657(13)70237-6
    [12] H. Deng, Multicriteria analysis for benchmarking sustainability development, Benchmarking, 22 (2015), 791–807.
    [13] A. Fahmi, F. Amin, S. Abdullah, A. Ali, Cubic fuzzy Einstein aggregation operators and its application to decision-making, Int. J. Syst. Sci., 49 (2018), 2385–2397. https://doi.org/10.1080/00207721.2018.1503356 doi: 10.1080/00207721.2018.1503356
    [14] I. Gallego, The use of economic, social and environmental indicators as a measure of sustainable development in Spain, Corp. Soc. Resp. Env. Ma., 13 (2006), 78–97.
    [15] J. Gualandris, M. Kalchschmidt, Customer pressure and innovativeness: Their role in sustainable supply chain management, J. Purch. Supply Manag., 20 (2014), 92–103. https://doi.org/10.1016/j.pursup.2014.03.001 doi: 10.1016/j.pursup.2014.03.001
    [16] J. L. Glover, D. Champion, K. J. Daniels, A. J. D. Dainty, Institutional theory perspective on sustainable practices across the dairy supply chain, Int. J. Prod. Econ., 152 (2014), 102–111. https://doi.org/10.1016/j.ijpe.2013.12.027 doi: 10.1016/j.ijpe.2013.12.027
    [17] K. Govindan, S. Rajendran, J. Sarkis, P. Murugesan, Multi criteria decision making approaches for green supplier evaluation and selection: A literature review, J. Clean. Prod., 98 (2015), 66–83.
    [18] H. Garg, K. Kumar, An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making, Soft Comput., 22 (2018), 4959–4970.
    [19] H. Garg, Some robust improved geometric aggregation operators under interval-valued intuitionistic fuzzy environment for multi-criteria decision-making process, J. Ind. Manag. Optim., 14 (2018), 283. https://doi.org/10.1007/s11428-018-0347-6 doi: 10.1007/s11428-018-0347-6
    [20] T. B. Garlet, J. L. D. Ribeiro, F. D. S. Savian, J. C. M. Siluk, Paths and barriers to the diffusion of distributed generation of photovoltaic energy in southern Brazil, Renew. Sust. Energ. Rev., 111 (2019), 157–169.
    [21] Y. B. Jun, C. S. Kim, K. O. Yang, Cubic sets, Ann. Fuzzy Math. Inform., 4 (2012), 83–98. https://doi.org/10.1177/0027432112446926 doi: 10.1177/0027432112446926
    [22] G. Kannan, S. Pokharel, P. S. Kumar, A hybrid approach using ISM and fuzzy TOPSIS for the selection of reverse logistics provider, Resour. Conserv. Recy., 54 (2009), 28–36.
    [23] G. Kou, D. Ergu, C. Lin, Y. Chen, Pairwise comparison matrix in multiple criteria decision making, Technol. Econ. Dev. Eco., 22 (2016), 738–765. https://doi.org/10.3846/20294913.2016.1210694 doi: 10.3846/20294913.2016.1210694
    [24] G. Kaur, H. Garg, Multi-attribute decision-making based on Bonferroni mean operators under cubic intuitionistic fuzzy set environment, Entropy, 20 (2018), 65. https://doi.org/10.3390/e20010065 doi: 10.3390/e20010065
    [25] G. Kaur, H, Garg, Cubic intuitionistic fuzzy aggregation operators, Int. J. Uncertain. Quan., 8 (2018), 405–427. https://doi.org/10.1615/Int.J.UncertaintyQuantification.2018020471 doi: 10.1615/Int.J.UncertaintyQuantification.2018020471
    [26] F. Khan, M. S. A. Khan, M. Shahzad, S. Abdullah, Pythagorean cubic fuzzy aggregation operators and their application to multi-criteria decision making problems, J. Intell. Fuzzy Syst. 36 (2019), 595–607. https://doi.org/10.3233/JIFS-18943 doi: 10.3233/JIFS-18943
    [27] G. Kaur, H. Garg, Generalized cubic intuitionistic fuzzy aggregation operators using t-norm operations and their applications to group decision-making process, Arab. J. Sci. Eng., 44 (2019), 2775–2794. https://doi.org/10.1007/s13369-018-3532-4 doi: 10.1007/s13369-018-3532-4
    [28] K. Kumar, H. Garg, Connection number of set pair analysis based TOPSIS method on intuitionistic fuzzy sets and their application to decision making, Appl. Intell., 48 (2018), 2112–2119. https://doi.org/10.1007/s10489-017-1067-0 doi: 10.1007/s10489-017-1067-0
    [29] R. O. Large, C. G. Thomsen, Drivers of green supply management performance: Evidence from Germany, J. Purch. Supply Manag., 17 (2011), 176–184. https://doi.org/10.1016/j.pursup.2011.04.006 doi: 10.1016/j.pursup.2011.04.006
    [30] R. J. Lin, Using fuzzy DEMATEL to evaluate the green supply chain management practices, J. Clean. Prod., 40 (2013), 32–39.
    [31] S. Liu, L. G. Papageorgiou, Multiobjective optimisation of production, distribution and capacity planning of global supply chains in the process industry, Omega, 41 (2013), 369–382. https://doi.org/10.1016/j.omega.2012.03.007 doi: 10.1016/j.omega.2012.03.007
    [32] L. Magee, A. Scerri, P. James, J. A. Thom, L. Padgham, S. Hickmott, et al., Reframing social sustainability reporting: Towards an engaged approach, Environ. Dev. Sustain., 15 (2013), 225–243. https://doi.org/10.1007/s10668-012-9384-2 doi: 10.1007/s10668-012-9384-2
    [33] T. Mahmood, F. Mehmood, Q. Khan, Cubic hesitant fuzzy sets and their applications to multi criteria decision making, Int. J. Algebra Statis., 5 (2016), 19–51.
    [34] T. Pinto-Varela, APFD. Barbosa-Póvoa, A. Q. Novais, Bi-objective optimization approach to the design and planning of supply chains: Economic versus environmental performances, Comput. Chem. Eng., 35 (2011), 1454–1468.
    [35] J. H. Park, H. J. Cho, Y. C. Kwun, Extension of the VIKOR method to dynamic intuitionistic fuzzy multiple attribute decision making, Comput. Math. Appl., 65 (2013), 731–744.
    [36] X. D. Peng, Y. Yang, Multiple attribute group decision making methods based on Pythagorean fuzzy linguistic set, Comput. Eng. Appl., 52 (2016), 50–54.
    [37] J. Qin, X. Liu, W. Pedrycz, An extended TODIM multi-criteria group decision making method for green supplier selection in interval type-2 fuzzy environment, Eur. J. Oper. Res., 258 (2017), 626–638.
    [38] E. Roghanian, S. J. Sadjadi, M. B. Aryanezhad, A probabilistic bi-level linear multi-objective programming problem to supply chain planning, Appl. Math. Comput., 188 (2007), 786–800.
    [39] M. Riaz, S. T. Tehrim, Cubic bipolar fuzzy ordered weighted geometric aggregation operators and their application using internal and external cubic bipolar fuzzy data, Comput. Appl. Math., 38 (2019), 1–25.
    [40] J. Sarkis, A boundaries and flows perspective of green supply chain management, Supply Chain Manag., 17 (2012), 202–216.
    [41] L. Shen, L. Olfat, K. Govindan, R. Khodaverdi, A. Diabat, A fuzzy multi criteria approach for evaluating green supplier's performance in green supply chain with linguistic preferences, Resour. Conserv. Recy., 74 (2013), 170–179.
    [42] V. K. Sharma, P. Chandna, A. Bhardwaj, Green supply chain management related performance indicators in agro industry: A review, J. Clean. Prod., 141 (2017), 1194–1208. https://doi.org/10.1016/j.jclepro.2016.09.103 doi: 10.1016/j.jclepro.2016.09.103
    [43] S. J. Wu, G. W. Wei, Pythagorean fuzzy Hamacher aggregation operators and their application to multiple attribute decision making, Int. J. Knowl.-Based In., 21 (2017), 189–201.
    [44] M. A. Sellitto, C. G. Camfield, S. Buzuku, Green innovation and competitive advantages in a furniture industrial cluster: A survey and structural model, Sustain. Prod. Consump., 23 (2020), 94–104.
    [45] M. A. Sellitto, F. K. Murakami, M. A. Butturi, S. Marinelli, N. Kadel, B. Rimini, Barriers, drivers, and relationships in industrial symbiosis of a network of Brazilian manufacturing companies, Sustain. Prod. Consump., 26 (2021), 443–454.
    [46] I. B. Turksen, Interval valued fuzzy sets based on normal forms, Fuzzy Set. Syst., 20 (1986), 191–210. https://doi.org/10.1016/0165-0114(86)90077-1 doi: 10.1016/0165-0114(86)90077-1
    [47] S. A. Torabi, E. Hassini, An interactive possibilistic programming approach for multiple objective supply chain master planning, Fuzzy Set. Syst., 159 (2008), 193–214. https://doi.org/10.1016/j.fss.2007.08.010 doi: 10.1016/j.fss.2007.08.010
    [48] M. L. Tseng, Green supply chain management with linguistic preferences and incomplete information, Appl. Soft Comput., 11 (2011), 4894–4903. https://doi.org/10.1016/j.asoc.2011.06.010 doi: 10.1016/j.asoc.2011.06.010
    [49] M. L. Tseng, A. S. F. Chiu, Grey-entropy analytical network process for green innovation practices, Procedia-Social Behav. Sci., 57 (2012), 10–21.
    [50] S. Thanki, K. Govindan, J. Thakkar, An investigation on lean-green implementation practices in Indian SMEs using analytical hierarchy process (AHP) approach, J. Clean. Prod., 135 (2016), 284–298. https://doi.org/10.1016/j.jclepro.2016.06.105 doi: 10.1016/j.jclepro.2016.06.105
    [51] S. Vachon, R. D. Klassen, Extending green practices across the supply chain: The impact of upstream and downstream integration, Int. J. Ope. Prod. Man., 26 (2006), 795–821.
    [52] X. Wang, E. Triantaphyllou, Ranking irregularities when evaluating alternatives by using some ELECTRE methods, Omega, 36 (2008), 45–63. https://doi.org/10.1016/j.omega.2005.12.003 doi: 10.1016/j.omega.2005.12.003
    [53] S. Wibowo, H. Deng, Intelligent decision support for effectively evaluating and selecting ships under uncertainty in marine transportation, Expert Syst. Appl., 39 (2012), 6911–6920.
    [54] S. Wibowo, H. Deng, Consensus-based decision support for multicriteria group decision making, Comput. Ind. Eng., 66 (2013), 625–633. https://doi.org/10.1016/j.cie.2013.09.015 doi: 10.1016/j.cie.2013.09.015
    [55] C. H. Yeh, H. Deng, S. Wibowo, Y. Xu, Fuzzy multicriteria decision support for information systems project selection, Int. J. Fuzzy Syst., 12 (2010), 170–174. https://doi.org/10.12968/nrec.2010.12.4.47097 doi: 10.12968/nrec.2010.12.4.47097
    [56] R. R. Yager, Pythagorean fuzzy subsets, 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), IEEE, 2013.
    [57] R. R. Yager, Pythagorean membership grades in multicriteria decision making, IEEE T. Fuzzy Syst., 22 (2013), 958–965.
    [58] M. G. M. Yang, P. Hong, S. B. Modi, Impact of lean manufacturing and environmental management on business performance: An empirical study of manufacturing firms, Int. J. Prod. Econ., 129 (2011), 251–261. https://doi.org/10.1016/j.ijpe.2010.10.017 doi: 10.1016/j.ijpe.2010.10.017
    [59] L. A. Zadeh, Fuzzy sets, Control Inform., 8 (1965), 338–353.
    [60] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-Ⅰ, Inform. Sciences, 8 (1975), 199–249. https://doi.org/10.1016/0020-0255(75)90036-5 doi: 10.1016/0020-0255(75)90036-5
    [61] Q. Zhu, J. Sarkis, An inter-sectoral comparison of green supply chain management in China: Drivers and practices. J. Clean. Prod., 14 (2006), 472–486. https://doi.org/10.1016/j.jclepro.2005.01.003 doi: 10.1016/j.jclepro.2005.01.003
    [62] Q. Zhu, J. Sarkis, K. Lai, Institutional-based antecedents and performance outcomes of internal and external green supply chain management practices, J. Purch. Supply Manag., 19 (2013), 106–117.
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