Abstract
Due to the increasing complexity and uncertainty in green supplier selection, there would be some hesitations for decision makers (DMs) to provide evaluation information of suppliers. Hesitant fuzzy set is a suitable tool to model such hesitations. This paper develops a hesitant fuzzy Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE) for multi-criteria group decision-making and applies to green supplier selection. First, a new hesitancy index of hesitant fuzzy element (HFE) is defined. Then, a generalized hesitant fuzzy Hausdorff distance is proposed considering the individual deviation of membership values and the hesitancy index simultaneously. A combined hesitant fuzzy entropy is presented integrating the defined fuzziness entropy and hesitancy entropy of HFEs. Subsequently, a linear programming model is established to derive DMs’ weights objectively. To determine the criteria weights for each DM, a nonlinear programming model is built through minimizing the relative entropy. The PROMETHEE is employed to obtain individual ranking of alternatives for each DM. To obtain the collective ranking of alternatives, a multi-objective assignment model is constructed and transformed into a single-objective assignment model for resolution. Thereby, a hesitant fuzzy PROMETHEE method is presented. A green supplier selection example is demonstrated to validate the proposed method.
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References
Awasthi A, Kannan G (2016) Green supplier development program selection using NGT and VIKOR under fuzzy environment. Comput Ind Eng 91:100–1088
Awasthi A, Chauhan SS, Goyal SK (2010) A fuzzy multicriteria approach for evaluating environmental performance of suppliers. Int J Prod Econ 126(2):370–378
Banaeian N, Mobli H, Fahimnia B et al (2018) Green supplier selection using fuzzy group decision making methods: a case study from the Agri-Food industry. Comput Oper Res 89:337–347
Bedregal B, Santiago RHN, Bustince H, Paternain D, Reiser R (2014a) Typical hesitant fuzzy negations. Int J Intell Syst 29(6):525–543
Bedregal B, Reiser R, Bustince H, Lopez-Molina C, Torra V (2014b) Aggregation functions for typical hesitant fuzzy elements and the action of automorphisms. Inf Sci 255:82–99
Bedregal B, Beliakov G, Bustince H, Calvo T, Mesiar R, Paternain D (2014c) A class of fuzzy multisets with a fixed number of memberships. Inf Sci 189:1–17
Beg I, Rashid T (2017) Modelling uncertainties in multi-criteria decision making using distance measure and topsis for hesitant fuzzy sets. J Artif Intell Soft Comput Res 7(2):103–109
Behzadian M, Kazemzadeh RB, Albadvi A et al (2010) PROMETHEE: a comprehensive literature review on methodologies and applications. Eur J Oper Res 200(1):198–215
Blome C, Hollos D, Paulraj A (2014) Green procurement and green supplier development: antecedents and effects on supplier performance. Int J Prod Res 52(1):32–49
Brans JP (1982) L’ingenierie de la décision. Elaboration d’instruments d’aide à la décision. Méthode PROMETHEE. In: Nadeau R, Landry M (eds) L’aide à la décision: nature. Instruments et Perspectives D’avenir. Presses de Université Laval, Québec, pp 183–214
Brans JP, Vincle P (1985) A preference ranking organization method. Manage Sci 31:647–656
Chen N, Xu Z (2015) Hesitant fuzzy ELECTRE II approach: a new way to handle multi-criteria decision making problems. Inf Sci 292:175–197
Chou SY, Chang YH (2008) A decision support system for supplier selection based on a strategy-aligned fuzzy SMART approach. Expert Syst Appl 34(4):2241–2253
Darabi S, Heydari J (2016) An interval-valued hesitant fuzzy ranking method based on group decision analysis for green supplier selection. IFAC Papersonline 49(2):12–17
Dickson GW (1966) An analysis of vender selection systems & decisions. J Purch 2(15):1377–1382
Dobos I, Vörösmarty G (2014) Green supplier selection and evaluation using DEA-type composite indicators. Int J Prod Econ 157:273–278
Dong JY, Wan SP (2016) Virtual enterprise partner selection integrating LINMAP and TOPSIS. J Oper Res Soc 67(10):1288–1308
Dong YC, Chen X, Herrera F (2015) Minimizing adjusted simple terms in the consensus reaching process with hesitant linguistic assessments in group decision making. Inf Sci 297:95–117
Dong YC, Li CC, Herrera F (2016) Connecting the linguistic hierarchy and the numerical scale for the 2-tuple linguistic model and its use to deal with hesitant unbalanced linguistic information. Inf Sci 367(368):259–278
Dong YC, Liu YT, Liang HM, Chiclana F, Herrera-Viedma E (2018) Strategic weight manipulation in multiple attribute decision making. Omega 75:154–164
Du B, Guo S, Huang X et al (2015) A Pareto supplier selection algorithm for minimum the life cycle cost of complex product system. Expert Syst Appl 42(9):4253–4264
Farhadinia B (2013) Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets. Inf Sci 240(10):129–144
Farhadinia B (2014) Distance and similarity measures for higher order hesitant fuzzy sets. Knowl Based Syst 55:43–48
Feng X, Tan Q, Zhang H (2015) PROMETHEE method for hesitant fuzzy multi-criteria decision making based on possibility degree. Sci Technol Rev 33(11):90–93
Ghorabaee MK, Zavadskas EK, Amiri M et al (2016) Multi-criteria evaluation of green suppliers using an extended WASPAS method with interval type-2 fuzzy sets. J Clean Prod 137:213–229
Govindan K, Jepsen MB (2016) ELECTRE: a comprehensive literature review on methodologies and applications. Eur J Oper Res 250(1):1–29
Govindan K, Kalyian M, Kannan D, Haq AN (2014) Barriers analysis for green supply chain management implementation in Indian industries using analytic hierarchy process. Int J Prod Econ 145:555–568
Govindan K, Rajendran S, Sarkis J et al (2015) Multi criteria decision making approaches for green supplier evaluation and selection: a literature review. J Clean Prod 98:66–83
Govindan K, Kadziński M, Sivakumar R (2017) Application of a novel PROMETHEE-based method for construction of a group compromise ranking to prioritization of green suppliers in food supply chain. Omega 71:129–145
Grisi RM, Guerra L, Naviglio G (2010) Supplier performance evaluation for green supply chain management: business Performance Measurement & Management. Springer, Berlin, pp 149–163
Gupta H, Barua MK (2017) Supplier selection among SMEs on the basis of their green innovation ability using BWM and fuzzy TOPSIS. J Clean Prod 152:242–258
Hamdan S, Cheaitou A (2017) Supplier selection and order allocation with green criteria: an MCDM and multi-objective optimization approach. Comput Oper Res 81:282–304
Hashemi SH, Karimi A, Tavana M (2015) An integrated green supplier selection approach with analytic network process and improved Grey relational analysis. Int J Prod Econ 159(159):178–191
He Y, Xu Z, Gu J (2016) An approach to group decision making with hesitant information and its application in credit risk evaluation of enterprises. Appl Soft Comput 43:159–169
Hosseini S, Barker K (2016) A Bayesian network model for resilience-based supplier selection. Int J Prod Econ 180:68–87
Hsu CW, Kuo TC, Chen SH et al (2013) Using DEMATEL to develop a carbon management model of supplier selection in green supply chain management. J Clean Prod 56(10):164–172
Hu J, Zhang X, Chen X, Liu Y (2016) Hesitant fuzzy information measures and their applications in multi-criteria decision making. Int J Syst Sci 47(1):62–76
Humphreys P, Mcivor R, Chan F (2003) Using case-based reasoning to evaluate supplier environmental management performance. Expert Syst Appl 25(2):141–153
Jain V, Kumar S, Kumar A et al (2016) An integrated buyer initiated decision-making process for green supplier selection. J Manuf Syst 41:256–265
Jauhar SK, Pant M (2017) Integrating DEA with DE and MODE for sustainable supplier selection. J Comput Sci 21:299–306
** F, Ni Z, Chen H, Li Y, Zhou L (2016) Multiple attribute group decision making based on interval-valued hesitant fuzzy information measures. Comput Ind Eng 101:103–115
Kannan D, Jabbour CJC (2014) Selecting green suppliers based on GSCM practices: using fuzzy TOPSIS applied to a Brazilian electronics company. Eur J Oper Res 233(2):432–447
Kannan D, Khodaverdi R, Olfat L et al (2013) Integrated fuzzy multi criteria decision making method and multi-objective programming approach for supplier selection and order allocation in a green supply chain. J Clean Prod 47(9):355–367
Kannan D, Govindan K, Rajendran S (2014) Fuzzy Axiomatic Design approach based green supplier selection: acase study from Singapore. J Clean Prod 96:194–208
Kou G, Lin CS (2014) A cosine maximization method for the priority vector derivation in AHP. Eur J Oper Res 235:225–232
Kou G, Liu YQ, Peng Y, Shi Y (2012) Evaluation of classification algorithms using MCDM and rank correlation. Int J Inf Technol Decis Mak 11(1):197–225
Kou G, Peng Y, Wang GX (2014a) Evaluation of clustering algorithms for financial risk analysis using MCDM methods. Inf Sci 27:1–12
Kou G, Ergu D, Shang J (2014b) Enhancing data consistency in decision matrix: adapting Hadamard model to mitigate judgment contradiction. Eur J Oper Res 236(1):261–271
Kou G, Ergu D, Lin CS, Chen Y (2016) Pairwise comparison matrix in multiple criteria decision making. Technol Econ Dev Econ 22(5):738–765
Kuo RJ, Wang YC, Tien FC (2010) Integration of artificial neural network and MADA methods for green supplier selection. J Clean Prod 18(12):1161–1170
Li W, Li B (2010) An extension of the Promethee II method based on generalized fuzzy numbers. Expert Syst Appl 37(7):5314–5319
Li D, Zeng W, Zhao Y (2015) Note on distance measure of hesitant fuzzy sets. Inf Sci 321:103–115
Li GX, Kou G, Peng Y (2016) A group decision making model for integrating heterogeneous information. IEEE Trans Syst Man Cybern Syst 1:1. https://doi.org/10.1109/TSMC.2016.2627050
Liao H, Xu Z (2014) Multi-criteria decision making with intuitionistic fuzzy PROMETHEE. J Intell Fuzzy Syst 27(4):1703–1717
Liu YT, Dong YC, Liang HM, Chiclana F, Herrera-Viedma E, Multiple attribute strategic weight manipulation with minimum cost in a group decision making context with interval attribute weights information. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/tsmc.2018.2874942 (in press)
Liu YT, Zhang H, Wu YC, Dong Y. Ranking range based approach to MADM under incomplete context and its application in venture investment evaluation. Technol Econ Dev Econ. https://doi.org/10.3846/tede.2019.10296 (in press)
Mahmoudi A, Soheil SN, Makui A et al (2016) An extension on PROMETHEE based on the typical hesitant fuzzy sets to solve multi-attribute decision-making problem. Kybernetes 45(8):1213–1231
Nielsen IE, Banaeian N, Golińska P et al (2014) Green supplier selection criteria: from a literature review to a flexible framework for determination of suitable criteria: logistics operations supply chain management and sustainability. Springer, Berlin, pp 79–99
Peng JJ, Wang JQ, Wu XH (2016) Novel multi-criteria decision-making approaches based on hesitant fuzzy sets and prospect theory. Int J Inf Technol Decis Mak 15(03):621–643
Qin J, Liu X, Pedrycz W (2017) An extended TODIM multi-criteria group decision making method for green supplier selection in interval type-2 fuzzy environment. Eur J Oper Res 258(2):626–638
Quirós P, Alonso P, Bustince H et al (2015) An entropy measure definition for finite interval-valued hesitant fuzzy sets. Knowl Based Syst 84:121–133
Roshandel J, Miri-Nargesi SS, Hatami-Shirkouhi L (2013) Evaluating and selecting the supplier in detergent production industry using hierarchical fuzzy TOPSIS. Appl Math Model 37(24):10170–10181
Sarkis J (1999) How green is the supply chain? Practice and research. Graduate School of Management. Clark University, Worchester, pp 1–40
Shang Y, Yuan XH, Lee ES (2010) The n-dimensional fuzzy sets and Zadeh fuzzy sets based on the finite valued fuzzy sets. Comput Math Appl 60(3):442–463
Thiruchelvam S, Tookey JE (2011) Evolving trends of suppliers election criteria and methods. Int J Automot Mech Eng 4:437–454
Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25(6):529–539
Torra V, Xu ZS, Herrera F (2014) Hesitant fuzzy sets: state of the art and future directions. Int J Intell Syst 29(6):495–524
Tsai WH, Hung SJ (2009) A fuzzy goal programming approach for green supply chain optimisation under activity-based costing and performance evaluation with a value-chain structure. Int J Prod Res 47(18):4991–5017
Weber CA, Current JR, Benton WC (1991) Vendor selection criteria and methods. Eur J Oper Res 50(1):2–18
Wei G, Wang HJ, Lin R (2011) Application of correlation coefficient to interval-valued intuitionistic fuzzy multiple attribute decision-making with incomplete weight information. Knowl Inf Syst 26(2):337–349
Wei C, Yan F, Rodríguez RM (2016) Entropy measures for hesitant fuzzy sets and their application in multi-criteria decision-making. J Intell Fuzzy Syst 31(1):673–685
Wu YZ, Li CC, Chen X, Dong YC (2018) Group decision making based on linguistic distributions and hesitant assessments: maximizing the support degree with an accuracy constraint. Inf Fusion 41:151–160
**a MM, Xu ZS (2011) Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 52(3):395–407
Xu ZS, **a MM (2011a) On distance and correlation measures of hesitant fuzzy information. Int J Intell Syst 26(5):410–425
Xu ZS, **a MM (2011b) Distance and similarity measures for hesitant fuzzy sets. Inf Sci 181(11):2128–2138
Xu ZS, **a MM (2012) Hesitant fuzzy entropy and cross-entropy and their use in multiattribute decision-making. Int J Intell Syst 27:799–822
Xu ZS, Zhang XL (2013) Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information. Knowl-Based Syst 52:53–64
Yan G (2009, Research on green suppliers’ evaluation based on AHP & genetic algorithm. In: International conference on signal processing systems. IEEE. pp 615–619
Yang JL, Tzeng GH (2011) An integrated MCDM technique combined with DEMATEL for a novel cluster-weighted with ANP method. Expert Syst Appl 38:1417–1424
Yeh WC, Chuang MC (2011) Using multi-objective genetic algorithm for partner selection in green supply chain problems. Expert Syst Appl 38(4):4244–4253
Yilmaz B, Dağdeviren M (2011) A combined approach for equipment selection: F-PROMETHEE method and zero–one goal programming. Expert Syst Appl 38(9):11641–11650
Zarandi MHF, Moghadam FS (2017) Fuzzy knowledge-based token-ordering policies for bullwhip effect management in supply chains. Knowl Inf Syst 50:607–631
Zhang Z (2013) Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making. Inf Sci 234:150–181
Zhang XL, Xu ZS (2014) The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment. Knowl-Based Syst 61:48–58
Zhang XL, Xu ZS (2015) Hesitant fuzzy QUALIFLEX approach with a signed distance-based comparison method for multiple criteria decision analysis. Expert Syst Appl 42(2):873–884
Zhang Q, **ng H, Liu F et al (2014) Some new entropy measures for interval-valued intuitionistic fuzzy sets based on distances and their relationships with similarity and inclusion measures. Inf Sci 283:55–69
Zhang F, Chen S, Li J et al (2018) New distance measures on hesitant fuzzy sets based on the cardinality theory and their application in pattern recognition. Soft Comput 22:1237–1245
Zhang HH, Kou G, Peng Y (2019) Soft consensus cost models for group decision making and economic interpretations. Eur J Oper Res 277:964–980
Zhu B, Xu ZS (2013) Hesitant fuzzy Bonferroni means for multi-criteria decision making. J Oper Res Soc 64(12):1831–1840
Acknowledgements
This research was supported by the National Natural Science Foundation of China (Nos. 71740021, 11861034 and 11461030), the Natural Science Foundation of Jiangxi Province of China (No. 20192BAB207012), the Science and Technology Project of Jiangxi province educational department of China (No. GJJ19), and “Thirteen five” Programming Project of Jiangxi province Social Science (2018) (No. 18GL13).
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Wan, Sp., Zou, Wc., Zhong, Lg. et al. Some new information measures for hesitant fuzzy PROMETHEE method and application to green supplier selection. Soft Comput 24, 9179–9203 (2020). https://doi.org/10.1007/s00500-019-04446-w
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DOI: https://doi.org/10.1007/s00500-019-04446-w