An integrated multi-criteria decision-making framework for sustainable supplier selection under picture fuzzy environment
Abstract
Sustainable supplier selection (SSS) is an important part of sustainable supply chain management (SSCM). In this paper, an integrated multi-criteria decision-making (MCDM) framework, based on the picture fuzzy exponential entropy, and the VIsekriterijumska optimizacija i KOmpromisno Resenje (VIKOR) method, is proposed to manage SSS problems. Firstly, the evaluation criteria of SSS, including economic, environmental and social, is established. This can be evaluated in the form of the actual data or linguistic terms provided by suppliers and experts respectively in an actual decision-making process. Then, according to the translated scales, all the evaluation information can be converted into picture fuzzy numbers (PFNs). Secondly, the picture fuzzy exponential entropy is defined. Moreover, based on the entropy’s minimization principle, the defined picture fuzzy exponential entropy is used to determine the weight of the SSS’s criteria. Thirdly, the extended VIKOR method, which combines the grey correlation coefficient, is utilized to select a suitable supplier. This method avoids the shortcomings of the traditional VIKOR method in data mining and solves the conflict between SSS criteria. Finally, the feasibility and effectiveness of the proposed integrated decision framework are verified by an experiment, as well as a sensitivity analysis and comparative analysis.
First published online 28 February 2020
Keyword : sustainable supplier selection, multi-criteria decision-making, picture fuzzy numbers, VIKOR, exponential entropy
How to Cite
Peng, J.- juan, Tian, C., Zhang, W.- yu, Zhang, S., & Wang, J.- qiang. (2020). An integrated multi-criteria decision-making framework for sustainable supplier selection under picture fuzzy environment. Technological and Economic Development of Economy, 26(3), 573-598. https://doi.org/10.3846/tede.2020.12110
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Aghdaie, M. H. (2017). Data mining group decision-making with fuzzy AHP: An application in supplier evaluation and segmentation. In Fuzzy analytic hierarchy process (pp. 77–102). Chapman and Hall/CRC. https://doi.org/10.1201/9781315369884-4
Alimardani, M., Hashemkhani Zolfani, S., Aghdaie, M. H., & Tamošaitienė, J. (2013). A novel hybrid SWARA and VIKOR methodology for supplier selection in an agile environment. Technological and Economic Development of Economy, 19(3), 533–548. https://doi.org/10.3846/20294913.2013.814606
Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3
Awasthi, A., Govindan, K., & Gold, S. (2018). Multi-tier sustainable global supplier selection using a fuzzy AHP-VIKOR based approach. International Journal of Production Economics, 195, 106–117. https://doi.org/10.1016/j.ijpe.2017.10.013
Bai, C. G., & Sarkis, J. (2010). Integrating sustainability into supplier selection with grey system and rough set methodologies. International Journal of Production Economics, 124(1), 252–264. https://doi.org/10.1016/j.ijpe.2009.11.023
Beskese, A., Kahraman, C., Ender Buyukbay, S., & Bozbura, F. T. (2018). An intiutionistic fuzzy multiexpert and multi-criteria system for effective performance management. Technological and Economic Development of Economy, 24(6), 2179–2201. https://doi.org/10.3846/tede.2018.6462
Chaharsooghi, S. K., & Ashrafi, M. (2014). Sustainable supplier performance evaluation and selection with neofuzzy TOPSIS method. International Scholarly Research Notices, 2014, 434168. https://doi.org/10.1155/2014/434168
Cheraghalipour, A., & Farsad, S. (2018). A bi-objective sustainable supplier selection and order allocation considering quantity discounts under disruption risks: A case study in plastic industry. Computers & Industrial Engineering, 118, 237–250. https://doi.org/10.1016/j.cie.2018.02.041
Cuong, B. C., & Kreinovich, V. (2013). Picture fuzzy sets-a new concept for computational intelligence problems. In Proc. of 3rd World Congress on Information and Communication Technologies (WICT) (pp. 1–6). https://doi.org/10.1109/WICT.2013.7113099
Elkington, J. (1998). Partnerships from cannibals with forks: the triple bottom line of 21 st-century business. Environmental Quality Management, 8(1), 37–51. https://doi.org/10.1002/tqem.3310080106
Goren, H. G. (2018). A decision framework for sustainable supplier selection and order allocation with lost sales. Journal of Cleaner Production, 183, 1156–1169. https://doi.org/10.1016/j.jclepro.2018.02.211
Hassini, E., Surti, C., & Searcy, C. (2012). A literature review and a case study of sustainable supply chains with a focus on metrics. International Journal of Production Economics, 140(1), 69–82. https://doi.org/10.1016/j.ijpe.2012.01.042
Ju, Y. B., Ju, D. W., Gonzalez, E. D. R., & Giannakis, S. M. (2019). Study of site selection of electric vehicle charging station based on extended GRP method under picture fuzzy environment. Computers & Industrial Engineering, 135, 1271–1285 https://doi.org/10.1016/j.cie.2018.07.048
Kannan, G., Roohollah, K., & Amin, V. (2015). Intuitionistic fuzzy based DEMATEL method for developing green practices and performances in a green supply chain. Expert Systems with Applications, 42(20), 7207–7220. https://doi.org/10.1016/j.eswa.2015.04.030
Kuo, R. J., Wang, Y. C., & Tien, F. C. (2010). Integration of artificial neural network and MADA methods for green supplier selection. Journal of Cleaner Production, 18(12), 1161–1170. https://doi.org/10.1016/j.jclepro.2010.03.020
Liu, K., Liu, Y. W., & Qin, J. D. (2018). An integrated ANP-VIKOR methodology for sustainable supplier selection with interval type-2 fuzzy sets. Granular Computing, 3(3), 193–208. https://doi.org/10.1007/s41066-017-0071-4
Liu, N., He, Y., & Xu, Z. (2019a). Evaluate Public-Private-Partnership’s advancement using double hierarchy hesitant fuzzy linguistic PROMETHEE with subjective and objective information from stakeholder perspective. Technological and Economic Development of Economy, 25(3), 386–420. https://doi.org/10.3846/tede.2019.7588
Liu, P., Rong, L., & Teng, F. (2019b). The evaluation of ecosystem health based on hybrid TODIM method for Chinese case. Technological and Economic Development of Economy, 25(3), 542–570. https://doi.org/10.3846/tede.2019.8021
Luo, L., Zhang, C., & Liao, H. C. (2019). Distance-based intuitionistic multiplicative MULTIMOORA method integrating a novel weight-determining method for multiple criteria group decision making. Computers & Industrial Engineering, 131, 82–98. https://doi.org/10.1016/j.cie.2019.03.038
Memaria, A., Dargi, A., Jokar, M. R. A., Ahmad, R., & Rahim, A. R. A. (2019). Sustainable supplier selection: A multi-criteria intuitionistic fuzzy TOPSIS method. Journal of Manufacturing Systems, 50, 9–24. https://doi.org/10.1016/j.jmsy.2018.11.002
Mou, N. Y., Chang, J. P., & Chen, Z. S. (2018). Sustainable supplier selection based on Pd-HFLTS and group decision-making theory. Computer Integrated Manufacturing Systems, 24(5), 1261–1278.
Opricovic, S., & Tzeng, G. H. (2004). Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS. European Journal of Operational Research, 156, 445–455. https://doi.org/10.1016/S0377-2217(03)00020-1
Osiro, L., Lima-Junior, F. R., & Carpinetti, L. C. R. (2018). A group decision model based on quality function deployment and hesitant fuzzy for selecting supply chain sustainability metrics. Journal of Cleaner Production, 183, 964–978. https://doi.org/10.1016/j.jclepro.2018.02.197
Peng, H. G., Shen, K. W., He, S. S., Zhang, H. Y., & Wang, J. Q. (2019). Investment risk evaluation for new energy resources: An integrated decision support model based on regret theory and ELECTRE III. Energy Conversion and Management, 183, 332–348. https://doi.org/10.1016/j.enconman.2019.01.015
Roostaee, R., Izadikhah, M., Lotfi, F. H., & Rostamy-Malkhalifeh, M. (2012). A multi-criteria intuitionistic fuzzy group decision making method for supplier selection with VIKOR Method. International Journal of Fuzzy System Applications, 2(1), 1–17. https://doi.org/10.4018/ijfsa.2012010101
Sanayei, A., Mousavi, S. F., & Yazdankhah, A. (2010). Group decision making process for supplier selection with VIKOR under fuzzy environment. Expert Systems with Applications, 37(1), 24–30. https://doi.org/10.1016/j.eswa.2009.04.063
Sarkis, J., & Dhavale, D. G. (2015). Supplier selection for sustainable operations: a triple-bottom-line approach using a Bayesian framework. International Journal of Production Economics, 166, 177–191. https://doi.org/10.1016/j.ijpe.2014.11.007
Scott, J. A., Ho, W., Dey, P. K., & Talluri, S. (2014). A decision support system for supplier selection and order allocation in stochastic, multi-stakeholder and multi-criteria environments. International Journal of Production Economics, 166, 226–237. https://doi.org/10.1016/j.ijpe.2014.11.008
Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27(3), 379–423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
Shen, K. W., Li, L., & Wang, J. Q. (2019a). Circular economy model for recycling waste resources under government participation: a case study in industrial waste water circulation in China. Technological and Economic Development of Economy, 26(1), 21–47. https://doi.org/10.3846/tede.2019.11249
Shen, K. W., Wang, X. K., Qiao, D., & Wang, J. Q. (2019b). Extended Z-MABAC method based on regret theory and directed distance for regional circular economy development program selection with Z-information. IEEE Transactions on Fuzzy Systems. https://doi.org/10.1109/TFUZZ.2019.2923948
Shen, K. W., & Wang, J. Q. (2018). Z-VIKOR method based on a new comprehensive weighted distance measure of Z-number and its application. IEEE Transactions on Fuzzy Systems, 26(6), 3232–3245. https://doi.org/10.1109/TFUZZ.2018.2816581
Tavana, M., Shabanpour, H., Yousefi, S., & Farzipoor, S. R. (2017). A hybrid goal programming and dynamic data envelopment analysis framework for sustainable supplier evaluation. Neural Computing and Applications, 28(12), 3683–3696. https://doi.org/10.1007/s00521-016-2274-z
Tian, C., & Peng, J. J. (2020). An integrated picture fuzzy ANP-TODIM multi-criteria decision-making approach for tourism attraction recommendation. Technological and Economic Development of Economy, 26(2), 331–354. https://doi.org/10.3846/tede.2019.11412
Tian, C., Peng, J. J., Zhang, W. Y., Zhang, S., & Wang, J. Q. (2020). Tourism environmental impact assessment based on improved AHP and picture fuzzy PROMETHEE II methods. Technological and Economic Development of Economy, 26(2), 355–378. https://doi.org/10.3846/tede.2019.11413
Tian, C., Peng, J. J., Zhang, S., Zhang, W. Y., & Wang, J. Q. (2019). Weighted picture fuzzy aggregation operators and their applications to multi-criteria decision-making problems. Computers & Industrial Engineering, 137, 106037. https://doi.org/10.1016/j.cie.2019.106037
Trapp, A. C., & Sarkis, J. (2016). Identifying robust portfolios of suppliers: a sustainability selection and development perspective. Journal of Cleaner Production, 112, 2088–2100. https://doi.org/10.1016/j.jclepro.2014.09.062
Wang, L., Peng, J. J., & Wang, J. Q. (2018). A multi-criteria decision-making framework for risk ranking of energy performance contracting project under picture fuzzy environment. Journal of Cleaner Production, 191, 105–118. https://doi.org/10.1016/j.jclepro.2018.04.169
Wang, R., Wang, J., Gao, H., & Wei, G. (2019a). Methods for MADM with picture fuzzy Muirhead mean operators and their application for evaluating the financial investment risk. Symmetry, 11(1), 6. https://doi.org/10.3390/sym11010006
Weber, C. A., & Desai, A. (1996). Determination of paths to vendor market efficiency using parallel coordinates representation: a negotiation tool for buyers. European Journal of Operational Research, 1, 142–155. https://doi.org/10.1016/0377-2217(94)00336-X
Weber, C. A., Current, J. R., & Benton, W. C. (1991). Vendor selection criteria and methods. European Journal of Operational Research, 50, 2–18. https://doi.org/10.1016/0377-2217(91)90033-R
Wei, G. W. (2016). Picture fuzzy cross-entropy for multiple attribute decision making problems. Journal of Business Economics and Management, 17(4), 491–502. https://doi.org/10.3846/16111699.2016.1197147
Wei, G. (2018). TODIM method for picture fuzzy multiple attribute decision making. Informatica, 29(3), 555–566. https://doi.org/10.15388/Informatica.2018.181
Wei, G., Alsaadi, F. E., Hayat, T., & Alsaedi, A. (2018). Projection models for multiple attribute decision making with picture fuzzy information. International Journal of Machine Learning and Cybernetics, 9(4), 713–719. https://doi.org/10.1007/s13042-016-0604-1
Wei, G. & Gao, H. (2018). The generalized Dice similarity measures for picture fuzzy sets and their applications. Informatica, 29(1), 107–124. https://doi.org/10.15388/Informatica.2018.160
Wang, L., Zhang, H. Y., Wang, J. Q., & Wu, G. F. (2019b). Picture fuzzy multi-criteria group decisionmaking method to hotel building energy efficiency retrofit project selection. RAIRO-Operations Research, 54(1), 211–229. https://doi.org/10.1051/ro/2019004
Wang, L., Wang, X. K., Peng, J. J., & Wang, J. Q. (2020). The differences in hotel selection among various types of travellers: A comparative analysis with a useful bounded rationality behavioural decision support model. Tourism Management, 76, 103961. https://doi.org/10.1016/j.tourman.2019.103961
Xu, Z., Qin, J. D., Liu, J., & Martínez, L. (2019). Sustainable supplier selection based on AHPSort II in interval type-2 fuzzy environment. Information Sciences, 483, 273–293. https://doi.org/10.1016/j.ins.2019.01.013
Yu, C., & Wong, T. N. (2015). An agent-based negotiation model for supplier selection of multiple products with synergy effect. Expert Systems with Applications, 42, 223–237. https://doi.org/10.1016/j.eswa.2014.07.057
Yu, C. X., Shao, Y. F., Wang, K., & Zhang, L. (2019). A group decision making sustainable supplier selection approach using extended TOPSIS under interval-valued Pythagorean fuzzy environment. Expert Systems with Applications, 12, 11–17. https://doi.org/10.1016/j.eswa.2018.12.010
Zhang, X. Y., Wang, J. Q., & Hu, J. H. (2018). On novel operational laws and aggregation operators of picture 2-tuple linguistic information for MCDM problems. International Journal of Fuzzy Systems, 20(3), 958–969. https://doi.org/10.1007/s40815-017-0441-8
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zhang, S., Wei, G., Gao, H., Wei, C., & Wei, Y. (2019a). EDAS method for multiple criteria group decision making with picture fuzzy information and its application to green suppliers selections. Technological and Economic Development of Economy, 25(6), 1123–1138. https://doi.org/10.3846/tede.2019.10714
Zhang, S., Gao, H., Wei, G., Wei, Y. & Wei, C. (2019b). Evaluation based on distance from average solution method for multiple criteria group decision making under picture 2-tuple linguistic environment. Mathematics, 7(3), 243. https://doi.org/10.3390/math7030243
Zhou, X., Pedrycz, W., Kuang, Y., & Zhang, Z. (2016). Type-2 fuzzy multi-objective DEA model: An application to sustainable supplier evaluation. Applied Soft Computing, 46, 424–440. https://doi.org/10.1016/j.asoc.2016.04.038
Alimardani, M., Hashemkhani Zolfani, S., Aghdaie, M. H., & Tamošaitienė, J. (2013). A novel hybrid SWARA and VIKOR methodology for supplier selection in an agile environment. Technological and Economic Development of Economy, 19(3), 533–548. https://doi.org/10.3846/20294913.2013.814606
Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3
Awasthi, A., Govindan, K., & Gold, S. (2018). Multi-tier sustainable global supplier selection using a fuzzy AHP-VIKOR based approach. International Journal of Production Economics, 195, 106–117. https://doi.org/10.1016/j.ijpe.2017.10.013
Bai, C. G., & Sarkis, J. (2010). Integrating sustainability into supplier selection with grey system and rough set methodologies. International Journal of Production Economics, 124(1), 252–264. https://doi.org/10.1016/j.ijpe.2009.11.023
Beskese, A., Kahraman, C., Ender Buyukbay, S., & Bozbura, F. T. (2018). An intiutionistic fuzzy multiexpert and multi-criteria system for effective performance management. Technological and Economic Development of Economy, 24(6), 2179–2201. https://doi.org/10.3846/tede.2018.6462
Chaharsooghi, S. K., & Ashrafi, M. (2014). Sustainable supplier performance evaluation and selection with neofuzzy TOPSIS method. International Scholarly Research Notices, 2014, 434168. https://doi.org/10.1155/2014/434168
Cheraghalipour, A., & Farsad, S. (2018). A bi-objective sustainable supplier selection and order allocation considering quantity discounts under disruption risks: A case study in plastic industry. Computers & Industrial Engineering, 118, 237–250. https://doi.org/10.1016/j.cie.2018.02.041
Cuong, B. C., & Kreinovich, V. (2013). Picture fuzzy sets-a new concept for computational intelligence problems. In Proc. of 3rd World Congress on Information and Communication Technologies (WICT) (pp. 1–6). https://doi.org/10.1109/WICT.2013.7113099
Elkington, J. (1998). Partnerships from cannibals with forks: the triple bottom line of 21 st-century business. Environmental Quality Management, 8(1), 37–51. https://doi.org/10.1002/tqem.3310080106
Goren, H. G. (2018). A decision framework for sustainable supplier selection and order allocation with lost sales. Journal of Cleaner Production, 183, 1156–1169. https://doi.org/10.1016/j.jclepro.2018.02.211
Hassini, E., Surti, C., & Searcy, C. (2012). A literature review and a case study of sustainable supply chains with a focus on metrics. International Journal of Production Economics, 140(1), 69–82. https://doi.org/10.1016/j.ijpe.2012.01.042
Ju, Y. B., Ju, D. W., Gonzalez, E. D. R., & Giannakis, S. M. (2019). Study of site selection of electric vehicle charging station based on extended GRP method under picture fuzzy environment. Computers & Industrial Engineering, 135, 1271–1285 https://doi.org/10.1016/j.cie.2018.07.048
Kannan, G., Roohollah, K., & Amin, V. (2015). Intuitionistic fuzzy based DEMATEL method for developing green practices and performances in a green supply chain. Expert Systems with Applications, 42(20), 7207–7220. https://doi.org/10.1016/j.eswa.2015.04.030
Kuo, R. J., Wang, Y. C., & Tien, F. C. (2010). Integration of artificial neural network and MADA methods for green supplier selection. Journal of Cleaner Production, 18(12), 1161–1170. https://doi.org/10.1016/j.jclepro.2010.03.020
Liu, K., Liu, Y. W., & Qin, J. D. (2018). An integrated ANP-VIKOR methodology for sustainable supplier selection with interval type-2 fuzzy sets. Granular Computing, 3(3), 193–208. https://doi.org/10.1007/s41066-017-0071-4
Liu, N., He, Y., & Xu, Z. (2019a). Evaluate Public-Private-Partnership’s advancement using double hierarchy hesitant fuzzy linguistic PROMETHEE with subjective and objective information from stakeholder perspective. Technological and Economic Development of Economy, 25(3), 386–420. https://doi.org/10.3846/tede.2019.7588
Liu, P., Rong, L., & Teng, F. (2019b). The evaluation of ecosystem health based on hybrid TODIM method for Chinese case. Technological and Economic Development of Economy, 25(3), 542–570. https://doi.org/10.3846/tede.2019.8021
Luo, L., Zhang, C., & Liao, H. C. (2019). Distance-based intuitionistic multiplicative MULTIMOORA method integrating a novel weight-determining method for multiple criteria group decision making. Computers & Industrial Engineering, 131, 82–98. https://doi.org/10.1016/j.cie.2019.03.038
Memaria, A., Dargi, A., Jokar, M. R. A., Ahmad, R., & Rahim, A. R. A. (2019). Sustainable supplier selection: A multi-criteria intuitionistic fuzzy TOPSIS method. Journal of Manufacturing Systems, 50, 9–24. https://doi.org/10.1016/j.jmsy.2018.11.002
Mou, N. Y., Chang, J. P., & Chen, Z. S. (2018). Sustainable supplier selection based on Pd-HFLTS and group decision-making theory. Computer Integrated Manufacturing Systems, 24(5), 1261–1278.
Opricovic, S., & Tzeng, G. H. (2004). Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS. European Journal of Operational Research, 156, 445–455. https://doi.org/10.1016/S0377-2217(03)00020-1
Osiro, L., Lima-Junior, F. R., & Carpinetti, L. C. R. (2018). A group decision model based on quality function deployment and hesitant fuzzy for selecting supply chain sustainability metrics. Journal of Cleaner Production, 183, 964–978. https://doi.org/10.1016/j.jclepro.2018.02.197
Peng, H. G., Shen, K. W., He, S. S., Zhang, H. Y., & Wang, J. Q. (2019). Investment risk evaluation for new energy resources: An integrated decision support model based on regret theory and ELECTRE III. Energy Conversion and Management, 183, 332–348. https://doi.org/10.1016/j.enconman.2019.01.015
Roostaee, R., Izadikhah, M., Lotfi, F. H., & Rostamy-Malkhalifeh, M. (2012). A multi-criteria intuitionistic fuzzy group decision making method for supplier selection with VIKOR Method. International Journal of Fuzzy System Applications, 2(1), 1–17. https://doi.org/10.4018/ijfsa.2012010101
Sanayei, A., Mousavi, S. F., & Yazdankhah, A. (2010). Group decision making process for supplier selection with VIKOR under fuzzy environment. Expert Systems with Applications, 37(1), 24–30. https://doi.org/10.1016/j.eswa.2009.04.063
Sarkis, J., & Dhavale, D. G. (2015). Supplier selection for sustainable operations: a triple-bottom-line approach using a Bayesian framework. International Journal of Production Economics, 166, 177–191. https://doi.org/10.1016/j.ijpe.2014.11.007
Scott, J. A., Ho, W., Dey, P. K., & Talluri, S. (2014). A decision support system for supplier selection and order allocation in stochastic, multi-stakeholder and multi-criteria environments. International Journal of Production Economics, 166, 226–237. https://doi.org/10.1016/j.ijpe.2014.11.008
Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27(3), 379–423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
Shen, K. W., Li, L., & Wang, J. Q. (2019a). Circular economy model for recycling waste resources under government participation: a case study in industrial waste water circulation in China. Technological and Economic Development of Economy, 26(1), 21–47. https://doi.org/10.3846/tede.2019.11249
Shen, K. W., Wang, X. K., Qiao, D., & Wang, J. Q. (2019b). Extended Z-MABAC method based on regret theory and directed distance for regional circular economy development program selection with Z-information. IEEE Transactions on Fuzzy Systems. https://doi.org/10.1109/TFUZZ.2019.2923948
Shen, K. W., & Wang, J. Q. (2018). Z-VIKOR method based on a new comprehensive weighted distance measure of Z-number and its application. IEEE Transactions on Fuzzy Systems, 26(6), 3232–3245. https://doi.org/10.1109/TFUZZ.2018.2816581
Tavana, M., Shabanpour, H., Yousefi, S., & Farzipoor, S. R. (2017). A hybrid goal programming and dynamic data envelopment analysis framework for sustainable supplier evaluation. Neural Computing and Applications, 28(12), 3683–3696. https://doi.org/10.1007/s00521-016-2274-z
Tian, C., & Peng, J. J. (2020). An integrated picture fuzzy ANP-TODIM multi-criteria decision-making approach for tourism attraction recommendation. Technological and Economic Development of Economy, 26(2), 331–354. https://doi.org/10.3846/tede.2019.11412
Tian, C., Peng, J. J., Zhang, W. Y., Zhang, S., & Wang, J. Q. (2020). Tourism environmental impact assessment based on improved AHP and picture fuzzy PROMETHEE II methods. Technological and Economic Development of Economy, 26(2), 355–378. https://doi.org/10.3846/tede.2019.11413
Tian, C., Peng, J. J., Zhang, S., Zhang, W. Y., & Wang, J. Q. (2019). Weighted picture fuzzy aggregation operators and their applications to multi-criteria decision-making problems. Computers & Industrial Engineering, 137, 106037. https://doi.org/10.1016/j.cie.2019.106037
Trapp, A. C., & Sarkis, J. (2016). Identifying robust portfolios of suppliers: a sustainability selection and development perspective. Journal of Cleaner Production, 112, 2088–2100. https://doi.org/10.1016/j.jclepro.2014.09.062
Wang, L., Peng, J. J., & Wang, J. Q. (2018). A multi-criteria decision-making framework for risk ranking of energy performance contracting project under picture fuzzy environment. Journal of Cleaner Production, 191, 105–118. https://doi.org/10.1016/j.jclepro.2018.04.169
Wang, R., Wang, J., Gao, H., & Wei, G. (2019a). Methods for MADM with picture fuzzy Muirhead mean operators and their application for evaluating the financial investment risk. Symmetry, 11(1), 6. https://doi.org/10.3390/sym11010006
Weber, C. A., & Desai, A. (1996). Determination of paths to vendor market efficiency using parallel coordinates representation: a negotiation tool for buyers. European Journal of Operational Research, 1, 142–155. https://doi.org/10.1016/0377-2217(94)00336-X
Weber, C. A., Current, J. R., & Benton, W. C. (1991). Vendor selection criteria and methods. European Journal of Operational Research, 50, 2–18. https://doi.org/10.1016/0377-2217(91)90033-R
Wei, G. W. (2016). Picture fuzzy cross-entropy for multiple attribute decision making problems. Journal of Business Economics and Management, 17(4), 491–502. https://doi.org/10.3846/16111699.2016.1197147
Wei, G. (2018). TODIM method for picture fuzzy multiple attribute decision making. Informatica, 29(3), 555–566. https://doi.org/10.15388/Informatica.2018.181
Wei, G., Alsaadi, F. E., Hayat, T., & Alsaedi, A. (2018). Projection models for multiple attribute decision making with picture fuzzy information. International Journal of Machine Learning and Cybernetics, 9(4), 713–719. https://doi.org/10.1007/s13042-016-0604-1
Wei, G. & Gao, H. (2018). The generalized Dice similarity measures for picture fuzzy sets and their applications. Informatica, 29(1), 107–124. https://doi.org/10.15388/Informatica.2018.160
Wang, L., Zhang, H. Y., Wang, J. Q., & Wu, G. F. (2019b). Picture fuzzy multi-criteria group decisionmaking method to hotel building energy efficiency retrofit project selection. RAIRO-Operations Research, 54(1), 211–229. https://doi.org/10.1051/ro/2019004
Wang, L., Wang, X. K., Peng, J. J., & Wang, J. Q. (2020). The differences in hotel selection among various types of travellers: A comparative analysis with a useful bounded rationality behavioural decision support model. Tourism Management, 76, 103961. https://doi.org/10.1016/j.tourman.2019.103961
Xu, Z., Qin, J. D., Liu, J., & Martínez, L. (2019). Sustainable supplier selection based on AHPSort II in interval type-2 fuzzy environment. Information Sciences, 483, 273–293. https://doi.org/10.1016/j.ins.2019.01.013
Yu, C., & Wong, T. N. (2015). An agent-based negotiation model for supplier selection of multiple products with synergy effect. Expert Systems with Applications, 42, 223–237. https://doi.org/10.1016/j.eswa.2014.07.057
Yu, C. X., Shao, Y. F., Wang, K., & Zhang, L. (2019). A group decision making sustainable supplier selection approach using extended TOPSIS under interval-valued Pythagorean fuzzy environment. Expert Systems with Applications, 12, 11–17. https://doi.org/10.1016/j.eswa.2018.12.010
Zhang, X. Y., Wang, J. Q., & Hu, J. H. (2018). On novel operational laws and aggregation operators of picture 2-tuple linguistic information for MCDM problems. International Journal of Fuzzy Systems, 20(3), 958–969. https://doi.org/10.1007/s40815-017-0441-8
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zhang, S., Wei, G., Gao, H., Wei, C., & Wei, Y. (2019a). EDAS method for multiple criteria group decision making with picture fuzzy information and its application to green suppliers selections. Technological and Economic Development of Economy, 25(6), 1123–1138. https://doi.org/10.3846/tede.2019.10714
Zhang, S., Gao, H., Wei, G., Wei, Y. & Wei, C. (2019b). Evaluation based on distance from average solution method for multiple criteria group decision making under picture 2-tuple linguistic environment. Mathematics, 7(3), 243. https://doi.org/10.3390/math7030243
Zhou, X., Pedrycz, W., Kuang, Y., & Zhang, Z. (2016). Type-2 fuzzy multi-objective DEA model: An application to sustainable supplier evaluation. Applied Soft Computing, 46, 424–440. https://doi.org/10.1016/j.asoc.2016.04.038