A Multi-criteria Picture Fuzzy Decision-making Model for Green Supplier Selection based on Fractional Programming

Guo Cao

Abstract


Due to the increasing complexity in green supplier selection, there would be some important issues for expressing inherent uncertainty or imprecision of decision makers’ cognitive information in decision making process. As an extension of intuitionistic fuzzy sets (IFSs) and neutrosophic sets (NSs), picture fuzzy sets (PFSs) can better model and represent the hesitancy and uncertainty of decision makers’ preference information. In this study, an attempt has been made to present a multi-criteria picture fuzzy decision-making model for green supplier selection based on fractional programming. In this approach, the ratings of alternatives and weights of criteria are represented by PFSs and IFSs, respectively. Based on the available information, some pairs of fractional programming models are derived from the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) and the proposed biparametric picture fuzzy distance measure to determine the relative closeness coefficient intervals of green suppliers, which are aggregated for the criteria to generate the ranking order of all green suppliers by computing their optimal degrees of membership based on the ranking method of interval numbers. Finally, an example is conducted to validate the effectiveness of the proposed multi-criteria decision making (MCMD) method.

Keywords


multi-criteria decision making (MCMD), picture fuzzy sets (PFSs), fractional programming, biparametric picture fuzzy distance measure, green supplier selection.

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References


Abdel-Basset, M.; Manogaran, G.; Gamal, A.; Smarandache, F. (2018). A hybrid approach of neutrosophic sets and DEMATEL method for developing supplier selection criteria, Design Automation for Embedded Systems, 22, 257-278, 2018.
https://doi.org/10.1007/s10617-018-9203-6

Akcan, S.; Tas, M. A. (2019). Green supplier evaluation with SWARA -TOPSIS integrated method to reduce ecological risk factors, Environmental Monitoring and Assessment, 191: 736, 2019.
https://doi.org/10.1007/s10661-019-7884-3

Atanassov, K. (1986). Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87--96, 1986.
https://doi.org/10.1016/S0165-0114(86)80034-3

Banaeian, N.; Mobli, H.; Fahimnia, B.; Nielsen, I. E. (2018). Green supplier selection using fuzzy group decision making methods, a case study from the agri-food industry, Computers & Operations Research, 89(1), 337--347, 2018.
https://doi.org/10.1016/j.cor.2016.02.015

Boran, F. E.; Akay, D. (2014). A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition, Information Sciences, 255, 45-57, 2014.
https://doi.org/10.1016/j.ins.2013.08.013

Celik, E.; Erdogan, M.; Gumus, A. T. (2016). An extended fuzzy TOPSIS-GRA method based on different separation measures for green logistics service provider selection, International Journal of Environmental Science and Technology, 13(5), 1377-1392, 2016.
https://doi.org/10.1007/s13762-016-0977-4

Cuong, B. C.; Kreinovich, V. (2013). Picture Fuzzy Sets-a new concept for computational intelligence problems, 2013 Third World Congress on Information and Communication Technologies (WICT 2013), 12: 1-6, 2013.
https://doi.org/10.1109/WICT.2013.7113099

Dzitac, I.; Filip, F.G.; Manolescu, M.J. (2017). Fuzzy Logic Is Not Fuzzy: World-renowned Computer Scientist Lofti A. Zadeh, International Journal of Computers Communications & Control, 12(6), 748-789, 2017.
https://doi.org/10.15837/ijccc.2017.6.3111

Eda, B.; Zahir, I.; Cengiz, K. (2018). Pythagorean fuzzy CODAS and its application to supplier selection in a manufacturing firm, Journal of Enterprise Information Management, 31(4), 550- 564, 2018.
https://doi.org/10.1108/JEIM-01-2018-0020

Fallahpour, A.; Olugu, E. U.; Musa, S. N.; Dariush, K.; Kuan, Y. W. (2016) An integrated model for green supplier selection under fuzzy environment: application of data envelopment analysis and genetic programming approach, Neural Computing & Applications, 27(3), 707-725, 2016.
https://doi.org/10.1007/s00521-015-1890-3

Gao, H. X.; Ju, Y. B.; Ernesto, S. G.; Zhang, W. K. (2020). Green supplier selection in electronics manufacturing: An approach based on consensus decision making, Journal of Cleaner Production, 245, 118781, 2020.
https://doi.org/10.1016/j.jclepro.2019.118781

Garg, H.; Arora, R. (2018). A nonlinear-programming methodology for multi- attribute decision making problem with interval-valued intuitionistic fuzzy soft sets information, Applied Intelligence, 48, 2031--2046, 2018.
https://doi.org/10.1007/s10489-017-1035-8

Gitinavard, H.; Ghaderi, H.; Pishvaee, M. S. (2018). Green supplier evaluation in manufacturing systems: a novel interval-valued hesitant fuzzy group outranking approach, Soft Computing, 3, 1-20, 2018.

Govindan, K.; Sivakumar, R. (2016). Green supplier selection and order allocation in a low carbon paper industry: integrated multi-criteria heterogeneous decision-making and multi-objective linear programming approaches, Annals of Operations Research, 238, 243--276, 2016.
https://doi.org/10.1007/s10479-015-2004-4

Karsak, E. E.; Dursun, M. (2015). An integrated fuzzy MCDM approach for supplier evaluation and selection, Computers & Industrial Engineering, 82: 82--93, 2015.
https://doi.org/10.1016/j.cie.2015.01.019

Li, J; Wang, J. Q. (2017). An extended QUALIFLEX method under probability hesitant fuzzy environment for selecting green suppliers, International Journal of Fuzzy Systems, 19(6), 1866- 1879, 2017.
https://doi.org/10.1007/s40815-017-0310-5

Liu, H. C.; Quan, M. Y.; Li, Z. W.; Wang, Z. L. (2019). A new integrated MCDM model for sustainable supplier selection under interval-valued intuitionistic uncertain linguistic environment, Information Sciences, 486, 254-270, 2019.
https://doi.org/10.1016/j.ins.2019.02.056

Liu, P. D.; Gao, H.; Ma, J. H. (2019). Novel green supplier selection method by combining quality function deployment with partitioned Bonferroni mean operator in interval type-2 fuzzy environment, Information Sciences, 490, 292--316, 2019.
https://doi.org/10.1016/j.ins.2019.03.079

Liu, P.; Wang, Y. (2014). Multiple attribute decision making method based on single-valued neutrosophic normalized weighted Bonferroni mean, Neural Computing & Applications, 25:2001- -2010, 2014.
https://doi.org/10.1007/s00521-014-1688-8

Lo, H. W.; Liou, J. J. H.; Wang, H. S.; Tsai, Y. S. (2018). An integrated model for solving problems in green supplier selection and order allocation, Journal of Cleaner Production, 190(20), 339-352, 2018.
https://doi.org/10.1016/j.jclepro.2018.04.105

Memaria, A.; Dargib, A.; Jokara, M. R. A.; Ahmadc, R.; Rahim, A. R. A. (2019). Sustainable supplier selection, A multi-criteria intuitionistic fuzzy TOPSIS method, Journal of Manufacturing Systems, 50, 9--24, 2019.
https://doi.org/10.1016/j.jmsy.2018.11.002

Mousakhani, S.; Nazari-Shirkouhi, S.; Bozorgi-Amiri, A. (2017). A novel interval type-2 fuzzy evaluation model based group decision analysis for green supplier selection problems: A case study of battery industry, Journal of Cleaner Production, 168, 205-218, 2017.
https://doi.org/10.1016/j.jclepro.2017.08.154

Pravin, K.; Rajesh, S. K.; Anurika, V. (2017). Suppliers' green performance evaluation using fuzzy extended ELECTRE approach, Clean Technologies and Environmental Policy, 19, 809--821, 2017.
https://doi.org/10.1007/s10098-016-1268-y

Rouyendegh, B. D.; Yildizbasi, A.; Üstünyer, P. (2019). Intuitionistic fuzzy TOPSIS method for green supplier selection problem, Soft Computing, DOI:
https://doi.org/10.1007/s00500-019- 04054-8, 2019.

Shen, L. X.; Olfat, L.; Govindan, K.; Khodaverdi, R.; Diabat, A. (2013). A fuzzy multi criteria approach for evaluating green supplier' s performance in green supply chain with linguistic preferences, Resources, Conservation & Recycling, 74, 170-179, 2013.
https://doi.org/10.1016/j.resconrec.2012.09.006

Son, L. H. (2015). DPFCM, A novel distributed picture fuzzy clustering method on picture fuzzy sets, Expert Systems with Applications, 42, 51-66, 2015.
https://doi.org/10.1016/j.eswa.2014.07.026

Wang, L.; Zhang, H. Y.; Wang, J. Q.; Li, L. (2017). Picture fuzzy normalized projection based VIKOR method for the risk evaluation of construction project, Applied Soft Computing, 64, 216--226, 2017.
https://doi.org/10.1016/j.asoc.2017.12.014

Wu, J.; Liu, Y. J. (2013). An approach for multiple attribute group decision making problems with interval-valued intuitionistic trapezoidal fuzzy numbers, Computers & Industrial Engineering, 66, 311--324, 2013.
https://doi.org/10.1016/j.cie.2013.07.001

Wu, Q.; Zhou, L.; Chen, Y.; Chen, H. Y. (2019). An integrated approach to green supplier selection based on the interval type-2 fuzzy best-worst and extended VIKOR methods, Information Sciences, 502, 394-417, 2019.
https://doi.org/10.1016/j.ins.2019.06.049

Xu, Z. S. (2011). A ranking arithmetic for fuzzy mutual complementary judgment matrices, Journal of Systems Engineering, 16 (4), 311-314, 2001.

Xu, Z. S.; Da, Q. L. (2003). A likelihood based method for priorities of interval judgment matrices, Chinese Journal of Management Science, 11, 63--65, 2003.

Zeng, S. Z.; Chen, S. M.; Wei, K. L. (2019). Multi-attribute decision making based on novel score function of intuitionistic fuzzy values and modified VIKOR method, Information Sciences, 488, 76--92, 2019.
https://doi.org/10.1016/j.ins.2019.03.018




DOI: https://doi.org/10.15837/ijccc.2020.1.3762



Copyright (c) 2020 Guo Cao

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