Large-Scale Green Supplier Selection Approach under a Q-Rung Interval-Valued Orthopair Fuzzy Environment
Abstract
:1. Introduction
2. Literature Reviews
2.1. GSS Approaches
2.2. Q-RIVOFS
2.3. Large-Scale GDM Problems
3. Preliminaries
3.1. Q-RIVOFS
- (1)
- If, then;
- (2)
- If, then:
- a.
- if, then;
- b.
- if, then.
3.2. Distance Measure of q-RIVOFS
- (1)
- (2)
- , if and only if;
- (3)
3.3. The Q-rung Interval-Valued Orthopair Fuzzy Weighted Aggregation Operators
4. The Proposed Large-Scale GSS Approach
4.1. Clustering Process of Large-Scale Decision Makers
4.2. Aggregation Process of Individual Evaluation Information
4.3. Determination Process of the Criteria Weights
4.4. Ranking Process Using the q-RIVOF-MULTIMOORA Approach
5. Case Study
5.1. Implementation
5.2. Sensitivity Analysis
5.3. Discussion
- (1)
- The q-RIVOFNs are introduced to evaluate green suppliers, which can not only represent the positive, negative, and indeterminacy membership levels of decision makers, simultaneously, but also relax the evaluation environment of decision makers. Furthermore, because of three degrees above are expressed by interval numbers, the uncertainty of evaluation information can be characterized effectively.
- (2)
- With the GSS issues becoming more and more complex, the scale of the decision maker team will become bigger and bigger. Considering the situation of large-scale decision makers participating in the evaluation mission, a clustering method with a deletetion mechanism is constructed to aggregate the evaluation information, which can reduce the negative impact of the non-consensus opinions on the ranking of green suppliers.
- (3)
- The q-RIVOFWA operator, the weighted Chebyshev distance of q-RIVOFNs, and the q-RIVOFWG operator are introduced to improve the ratio system, the reference point approach, and the full multiplicative form of MULTIMOORA approach, respectively. Subsequently, the q-RIVOF-MULTIMOORA approach is developed to rank green suppliers, in which the weight vector of criteria is highlighted during the ranking process, and the robustness of the ranking result is relatively strong.
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
- Rostamzadeh, R.; Govindan, K.; Esmaeili, A.; Sabaghi, M. Application of fuzzy VIKOR for evaluation of green supply chain management practices. Ecol. Indic. 2015, 49, 188–203. [Google Scholar] [CrossRef]
- Sahu, N.K.; Datta, S.; Mahapatra, S.S. Establishing green supplier appraisement platform using grey concepts. Grey Syst. 2012, 2, 395–418. [Google Scholar] [CrossRef]
- Vachon, S. Green supply chain practices and the selection of environmental technologies. Int. J. Prod. Res. 2007, 45, 4357–4379. [Google Scholar] [CrossRef]
- Cabral, I.; Grilo, A.; Cruz-Machado, V. A decision-making model for lean, agile, resilient and green supply chain management. Int. J. Prod. Res. 2012, 50, 4830–4845. [Google Scholar] [CrossRef]
- Beamon, B.M. Designing the green supply chain. Logist. Inf. Manag. 2013, 12, 332–342. [Google Scholar] [CrossRef]
- Bai, C.; Sarkis, J. Green supplier development: Analytical evaluation using rough set theory. J. Clean. Prod. 2010, 18, 1200–1210. [Google Scholar] [CrossRef]
- Kannan, D.; Govindan, K.; Rajendran, S. Fuzzy axiomatic design approach based green supplier selection: A case study from Singapore. J. Clean. Prod. 2015, 96, 194–208. [Google Scholar] [CrossRef]
- Blome, C.; Hollos, D.; Paulraj, A. Green procurement and green supplier development: Antecedents and effects on supplier performance. Int. J. Prod. Res. 2014, 52, 32–49. [Google Scholar] [CrossRef]
- Govindan, K.; Rajendran, S.; Sarkis, J.; Murugesan, P. Multi criteria decision making approaches for green supplier evaluation and selection: A literature review. J. Clean. Prod. 2015, 98, 66–83. [Google Scholar] [CrossRef]
- Moheb-Alizadeh, H.; Handfield, R. Sustainable supplier selection and order allocation: A novel multi-objective programming model with a hybrid solution approach. Comput. Ind. Eng. 2019, 129, 192–209. [Google Scholar] [CrossRef]
- Moheb-Alizadeh, H.; Handfield, R. An integrated chance-constrained stochastic model for efficient and sustainable supplier selection and order allocation. Int. J. Prod. Res. 2018, 56, 6890–6916. [Google Scholar] [CrossRef]
- Qin, J.; Liu, X.; Pedrycz, W. An extended TODIM multi-criteria group decision making method for green supplier selection in interval type-2 fuzzy environment. Eur. J. Oper. Res. 2017, 258, 626–638. [Google Scholar] [CrossRef]
- Zhu, J.; Li, Y.; Rosen, M.A. Green supplier selection based on consensus process and integrating prioritized operator and Choquet integral. Sustainability 2018, 10, 2744. [Google Scholar] [CrossRef]
- Wang, J.; Wei, G.W.; Wei, Y. Models for green supplier selection with some 2-tuple linguistic neutrosophic number Bonferroni mean operators. Symmetry 2018, 10, 131. [Google Scholar] [CrossRef]
- Banaeian, N.; Mobli, H.; Fahimnia, B.; Nielsen, I.E.; Omid, M. Green supplier selection using fuzzy group decision making methods: A case study from the agri-food industry. Comput. Oper. Res. 2018, 89, 337–347. [Google Scholar] [CrossRef]
- Ghorabaee, M.K.; Zavadskas, E.K.; Amiri, M.; Esmaeili, A. Multi-criteria evaluation of green suppliers using an extended WASPAS method with interval type-2 fuzzy sets. J. Clean. Prod. 2016, 137, 213–229. [Google Scholar] [CrossRef]
- Cao, Q.; Wu, J.; Liang, C. An intuitionsitic fuzzy judgement matrix and TOPSIS integrated multi-criteria decision making method for green supplier selection. J. Intell. Fuzzy Syst. 2015, 28, 117–126. [Google Scholar]
- Yager, R.R. Generalized orthopair fuzzy sets. IEEE Trans. Fuzzy Syst. 2017, 25, 1222–1230. [Google Scholar] [CrossRef]
- Wang, R.; Li, Y. A novel approach for green supplier selection under a q-rung orthopair fuzzy environment. Symmetry 2018, 10, 687. [Google Scholar] [CrossRef]
- Liu, P.; Liu, J. Some q-rung orthopair fuzzy Bonferroni mean operators and their application to multi-attribute group decision making. Int. J. Intell. Syst. 2018, 33, 315–347. [Google Scholar] [CrossRef]
- Wei, G.; Gao, H.; Wei, Y. Some q-rung orthopair fuzzy Heronian mean operators in multiple attribute decision making. Int. J. Intell. Syst. 2018, 33, 1426–1458. [Google Scholar] [CrossRef]
- Joshi, B.P.; Singh, A.; Bhatt, P.K.; Vaisla, K.S. Interval valued q-rung orthopair fuzzy sets and their properties. J. Intell. Fuzzy Syst. 2018, 35, 5225–5230. [Google Scholar] [CrossRef]
- Wang, J.; Gao, H.; Wei, G.; Wei, Y. Methods for multiple-attribute group decision making with q-rung interval-valued orthopair fuzzy information and their applications to the selection of green suppliers. Symmetry 2019, 11, 56. [Google Scholar] [CrossRef]
- Liu, H.C.; You, X.Y.; Tsung, F.; Ji, P. An improved approach for failure mode and effect analysis involving large group of experts: An application to the healthcare field. Qual. Eng. 2018, 30, 762–775. [Google Scholar] [CrossRef]
- Xu, X.H.; Du, Z.J.; Chen, X.H. Consensus model for multi-criteria large-group emergency decision making considering non-cooperative behaviors and minority opinions. Decis. Support Syst. 2015, 79, 150–160. [Google Scholar] [CrossRef]
- Wu, Z.; Xu, J. A consensus model for large-scale group decision making with hesitant fuzzy information and changeable clusters. Inf. Fusion 2018, 41, 217–231. [Google Scholar] [CrossRef]
- Brauers, W.K.M. Project management for a country with multiple objectives. Czech Econ. Rev. 2012, 6, 80–101. [Google Scholar]
- Brauers, W.K.M.; Zavadskas, E.K. Project management by MULTIMOORA as an instrument for transition economies. Technol. Econ. Dev. Econ. 2010, 16, 5–24. [Google Scholar] [CrossRef]
- Li, Y.L.; Wang, R.; Chin, K.S. New failure mode and effect analysis approach considering consensus under interval-valued intuitionistic fuzzy environment. Soft Comput. 2019. [Google Scholar] [CrossRef]
- Zhao, H.; You, J.X.; Liu, H.C. Failure mode and effect analysis using MULTIMOORA method with continuous weighted entropy under interval-valued intuitionistic fuzzy environment. Soft Comput. 2017, 21, 5355–5367. [Google Scholar] [CrossRef]
- Baležentis, T.; Baležentis, A. A survey on development and applications of the multi-criteria decision making method MULTIMOORA. J. Multi-Criteria Decis. Anal. 2014, 21, 209–222. [Google Scholar]
- Deshmukh, S.; Sunnapwar, V. Fuzzy analytic hierarchy process (FAHP) for green supplier selection in Indian industries. In Proceedings of the International Conference on Intelligent Manufacturing and Automation, Tokyo, Japan, 27–30 September 2019; Springer: Singapore, 2019; pp. 679–687. [Google Scholar]
- Dobos, I.; Vörösmarty, G. Evaluating green suppliers: Improving supplier performance with DEA in the presence of incomplete data. Cent. Eur. J. Oper. Res. 2019, 27, 483–495. [Google Scholar] [CrossRef]
- Dobos, I.; Vörösmarty, G. Inventory-related costs in green supplier selection problems with data envelopment analysis (DEA). Int. J. Prod. Econ. 2019, 209, 374–380. [Google Scholar] [CrossRef]
- Govindan, K.; Kadziński, M.; Sivakumar, R. Application of a novel PROMETHEE-based method for construction of a group compromise ranking to prioritization of green suppliers in food supply chain. Omega 2016, 71, 129–145. [Google Scholar] [CrossRef]
- Matić, B.; Jovanović, S.; Das, D.K.; Zavadskas, E.K.; Stević, Ž.; Sremac, S.; Marinković, M. A new hybrid MCDM model: Sustainable supplier selection in a construction company. Symmetry 2019, 11, 353. [Google Scholar] [CrossRef]
- Liu, H.C.; Quan, M.Y.; Li, Z.; Wang, Z.L. A new integrated MCDM model for sustainable supplier selection under interval-valued intuitionistic uncertain linguistic environment. Inf. Sci. 2019, 486, 254–270. [Google Scholar] [CrossRef]
- Yucesan, M.; Mete, S.; Serin, F.; Celik, E.; Gul, M. An integrated best-worst and interval type-2 fuzzy TOPSIS methodology for green supplier selection. Mathematics 2019, 7, 182. [Google Scholar] [CrossRef]
- Tsui, C.W.; Wen, U.P. A hybrid multiple criteria group decision-making approach for green supplier selection in the TFT-LCD industry. Math. Probl. Eng. 2014, 2014, 709872. [Google Scholar] [CrossRef]
- Abdel-Baset, M.; Chang, V.; Gamal, A.; Smarandache, F. An integrated neutrosophic ANP and VIKOR method for achieving sustainable supplier selection: A case study in importing field. Comput. Ind. 2019, 106, 94–110. [Google Scholar] [CrossRef]
- Hashemi, S.H.; Karimi, A.; Tavana, M. An integrated green supplier selection approach with analytic network process and improved grey relational analysis. Int. J. Prod. Econ. 2015, 159, 178–191. [Google Scholar] [CrossRef]
- Kuo, T.C.; Hsu, C.W.; Li, J.Y. Developing a green supplier selection model by using the DANP with VIKOR. Sustainability 2015, 7, 1661–1689. [Google Scholar] [CrossRef]
- Liang, Y.; Liu, J.; Qin, J.; Tu, Y. An improved multi-granularity interval 2-tuple TODIM approach and its application to green supplier selection. Int. J. Fuzzy Syst. 2019, 21, 129–144. [Google Scholar] [CrossRef]
- Rashidi, K.; Cullinane, K. A comparison of fuzzy DEA and fuzzy TOPSIS in sustainable supplier selection: Implications for sourcing strategy. Expert Syst. Appl. 2019, 121, 266–281. [Google Scholar] [CrossRef]
- Zadeh, L.A. Fuzzy sets. Inf. Control 1965, 8, 338–353. [Google Scholar] [CrossRef] [Green Version]
- Zhou, X.; Pedrycz, W.; Kuang, Y.; Zhang, Z. Type-2 fuzzy multi-objective DEA model: An application to sustainable supplier evaluation. Appl. Soft Comput. 2016, 46, 424–440. [Google Scholar] [CrossRef]
- Atanassov, K.T. Intuitionistic fuzzy sets. Fuzzy Sets Syst. 1986, 20, 87–96. [Google Scholar] [CrossRef]
- Atanassov, K.T. Interval valued intuitionistic fuzzy sets. In Intuitionistic Fuzzy Sets; Publisher Name Physica: Heidelberg, Germany, 1999; pp. 139–177. [Google Scholar]
- Yager, R.R. Pythagorean membership grades in multicriteria decision making. IEEE Trans. Fuzzy Syst. 2013, 22, 958–965. [Google Scholar] [CrossRef]
- Peng, X.; Yang, Y. Fundamental properties of interval-valued Pythagorean fuzzy aggregation operators. Int. J. Intell. Syst. 2016, 31, 444–487. [Google Scholar] [CrossRef]
- Zhang, Z.; Guo, C.; Martínez, L. Managing multigranular linguistic distribution assessments in large-scale multiattribute group decision making. IEEE Trans. Syst. ManCybern. Syst. 2016, 47, 3063–3076. [Google Scholar] [CrossRef]
- Palomares, I.; Martinez, L.; Herrera, F. A consensus model to detect and manage noncooperative behaviors in large-scale group decision making. IEEE Trans. Fuzzy Syst. 2013, 22, 516–530. [Google Scholar] [CrossRef]
- Liu, Y.; Fan, Z.P.; Zhang, X. A method for large group decision-making based on evaluation information provided by participators from multiple groups. Inf. Fusion 2016, 29, 132–141. [Google Scholar] [CrossRef] [Green Version]
- Labella, Á.; Liu, Y.; Rodríguez, R.M.; Martínez, L. Analyzing the performance of classical consensus models in large scale group decision making: A comparative study. Appl. Soft Comput. 2018, 67, 677–690. [Google Scholar] [CrossRef]
- Du, W.S. Minkowski-type distance measures for generalized orthopair fuzzy sets. Int. J. Intell. Syst. 2018, 33, 802–817. [Google Scholar] [CrossRef]
- Du, Y.; Hou, F.; Zafar, W.; Yu, Q.; Zhai, Y. A novel method for multiattribute decision making with interval-valued Pythagorean fuzzy linguistic information. Int. J. Intell. Syst. 2017, 32, 1085–1112. [Google Scholar] [CrossRef]
- Liu, B.; Shen, Y.; Zhang, W.; Chen, X.; Wang, X. An interval-valued intuitionistic fuzzy principal component analysis model-based method for complex multi-attribute large-group decision-making. Eur. J. Oper. Res. 2015, 245, 209–225. [Google Scholar] [CrossRef]
- Zhou, S.; Xu, X.; Zhou, Y.; Chen, X. A large group decision-making method based on fuzzy preference relation. Int. J. Inf. Technol. Decis. Mak. 2017, 16, 881–897. [Google Scholar] [CrossRef]
- Xu, X.H.; Zhong, X.Y.; Chen, X.H.; Zhou, Y.J. A dynamical consensus method based on exit–delegation mechanism for large group emergency decision making. Knowl.-Based Syst. 2015, 86, 237–249. [Google Scholar] [CrossRef]
- Zhu, J.; Zhang, S.; Chen, Y.; Zhang, L. A hierarchical clustering approach based on three-dimensional gray relational analysis for clustering a large group of decision makers with double information. Group Decis. Negot. 2016, 25, 325–354. [Google Scholar] [CrossRef]
- Cai, C.G.; Xu, X.H.; Wang, P.; Chen, X.H. A multi-stage conflict style large group emergency decision-making method. Soft Comput. 2017, 21, 5765–5778. [Google Scholar] [CrossRef]
- Fishburn, P.C.; Gehrlein, W.V. Borda’s rule, positional voting, and condorcet’s simple majority principle. Public Choice 1976, 28, 79–88. [Google Scholar] [CrossRef]
- Alonso, S.; Herrera-Viedma, E.; Chiclana, F.; Herrera, F. A web based consensus support system for group decision making problems and incomplete preferences. Inf. Sci. 2010, 180, 4477–4495. [Google Scholar] [CrossRef]
- Chiclana, F.; Mata, F.; Martínez, L.; Herrera-Viedma, E.; Alonso, S. Integration of a consistency control module within a consensus model. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 2008, 16, 35–53. [Google Scholar] [CrossRef]
- Zhang, H.Y.; Ji, P.; Wang, J.Q.; Chen, X.H. An improved weighted correlation coefficient based on integrated weight for interval neutrosophic sets and its application in multi-criteria decision-making problems. Int. J. Comput. Intell. Syst. 2015, 8, 1027–1043. [Google Scholar] [CrossRef]
- Zhang, X.; Jin, F.; Liu, P. A grey relational projection method for multi-attribute decision making based on intuitionistic trapezoidal fuzzy number. Appl. Math. Model. 2013, 37, 3467–3477. [Google Scholar] [CrossRef]
Linguistic Terms | Corresponding q-RIVOFNs |
---|---|
Extremely High (EH) | ([0.90,0.95], [0.10,0.15]) |
Very High (VH) | ([0.80,0.85], [0.20,0.25]) |
High (H) | ([0.70,0.75], [0.30,0.35]) |
Medium High (MH) | ([0.60,0.65], [0.40,0.45]) |
Medium (M) | ([0.50,0.55], [0.50,0.55]) |
Medium Low (ML) | ([0.40,0.45], [0.60,0.65]) |
Low (L) | ([0.30,0.35], [0.70,0.75]) |
Very Low (VL) | ([0.20,0.25], [0.80,0.85]) |
Extremely Low (EL) | ([0.10,0.15], [0.90,0.95]) |
Decision Makers | Green Suppliers | Criteria | |||
---|---|---|---|---|---|
C1 | C2 | C3 | C4 | ||
DM1 | G1 | H | M | H | L |
G2 | M | MH | VH | EL | |
G3 | ML | VH | M | M | |
G4 | VH | M | M | MH | |
G5 | L | ML | ML | H | |
DM2 | G1 | VL | H | ML | L |
G2 | MH | L | VH | MH | |
G3 | M | VH | MH | VH | |
G4 | VH | VH | MH | MH | |
G5 | H | ML | ML | H | |
DM3 | G1 | VH | M | MH | EL |
G2 | M | MH | VH | EL | |
G3 | ML | VH | M | MH | |
G4 | VH | M | ML | MH | |
G5 | VL | ML | ML | MH | |
DM4 | G1 | H | M | EH | EH |
G2 | ML | H | VL | EL | |
G3 | ML | VL | M | ML | |
G4 | L | ML | M | VL | |
G5 | L | H | MH | L | |
DM5 | G1 | H | M | H | L |
G2 | M | M | EH | EL | |
G3 | ML | VH | ML | M | |
G4 | VH | ML | M | H | |
G5 | L | ML | ML | MH | |
DM6 | G1 | H | ML | EH | EH |
G2 | ML | MH | VL | EL | |
G3 | ML | VL | MH | ML | |
G4 | L | ML | M | L | |
G5 | L | H | H | L | |
DM7 | G1 | L | H | ML | L |
G2 | M | L | VH | H | |
G3 | M | H | MH | VH | |
G4 | VH | VH | M | MH | |
G5 | H | ML | ML | H | |
DM8 | G1 | VH | M | EH | EH |
G2 | ML | H | VL | EL | |
G3 | ML | L | MH | ML | |
G4 | ML | L | M | VL | |
G5 | L | H | MH | L | |
DM9 | G1 | H | MH | MH | L |
G2 | M | MH | VH | EL | |
G3 | ML | VH | M | MH | |
G4 | VH | ML | M | MH | |
G5 | L | ML | L | EH | |
DM10 | G1 | H | M | H | L |
G2 | M | MH | VH | EL | |
G3 | L | VH | ML | M | |
G4 | H | M | M | MH | |
G5 | L | ML | M | H | |
DM11 | G1 | H | H | H | L |
G2 | MH | L | L | EL | |
G3 | VH | VH | M | EL | |
G4 | VH | VL | M | H | |
G5 | VH | H | L | L | |
DM12 | G1 | VL | H | ML | L |
G2 | MH | L | VH | MH | |
G3 | ML | H | H | VH | |
G4 | VH | VH | MH | MH | |
G5 | MH | ML | ML | MH | |
DM13 | G1 | H | M | EH | EH |
G2 | L | H | VL | EL | |
G3 | ML | VL | M | ML | |
G4 | ML | ML | MH | VL | |
G5 | L | MH | MH | ML | |
DM14 | G1 | H | ML | H | VH |
G2 | VH | MH | VL | EL | |
G3 | ML | EH | MH | MH | |
G4 | M | EH | VL | ML | |
G5 | ML | ML | ML | H | |
DM15 | G1 | VL | H | ML | ML |
G2 | MH | ML | VH | MH | |
G3 | M | VH | MH | VH | |
G4 | H | VH | MH | H | |
G5 | H | ML | L | H | |
DM16 | G1 | H | M | H | EH |
G2 | ML | H | VL | L | |
G3 | ML | VL | VH | L | |
G4 | L | M | M | VL | |
G5 | L | H | MH | L | |
DM17 | G1 | VH | M | H | L |
G2 | M | MH | MH | EL | |
G3 | ML | VH | M | MH | |
G4 | VH | M | M | H | |
G5 | VL | ML | M | H | |
DM18 | G1 | H | ML | VH | VH |
G2 | H | L | L | VH | |
G3 | MH | VH | M | MH | |
G4 | VH | EH | M | VH | |
G5 | VL | ML | VH | H | |
DM19 | G1 | L | MH | ML | L |
G2 | MH | VL | VH | MH | |
G3 | M | H | MH | VH | |
G4 | VH | VH | MH | MH | |
G5 | H | ML | L | H | |
DM20 | G1 | EH | M | EL | L |
G2 | ML | VH | MH | EL | |
G3 | VH | VH | ML | M | |
G4 | VH | ML | VH | MH | |
G5 | H | VH | H | L |
Green Suppliers | ||||
---|---|---|---|---|
([0.7399,0.7909], [0.2621,0.3129]) | ([0.5203,0.5703], [0.4817,0.5319]) | ([0.6718,0.7221], [0.3302,0.3806]) | ([0.7566,0.8154], [0.2498,0.3039]) | |
([0.5000,0.5500], [0.5000,0.5500]) | ([0.5863,0.6363], [0.4152,0.4653]) | ([0.8048,0.8604], [0.2000,0.2532]) | ([0.9000,0.9500], [0.1000,0.1500]) | |
([0.3869,0.4367], [0.6156,0.6657]) | ([0.8000,0.8500], [0.2000,0.2500]) | ([0.4720,0.5217], [0.5313,0.5815]) | ([0.4563,0.5060], [0.5477,0.5979]) | |
([0.7869,0.8374], [0.2140,0.2644]) | ([0.4720,0.5217], [0.5313,0.5815]) | ([0.4865,0.5363], [0.5154,0.5655]) | ([0.3728,0.4223], [0.6316,0.6818]) | |
([0.2746,0.3236], [0.7319,0.7820]) | ([0.4000,0.4500], [0.6000,0.6500]) | ([0.4288,0.4781], [0.5793,0.6296]) | ([0.3279,0.3753], [0.6934,0.7438]) |
Green Suppliers | ||||
---|---|---|---|---|
([0.2501,0.2986], [0.7584,0.8085]) | ([0.6835,0.7337], [0.3178,0.3680]) | ([0.4000,0.4500], [0.6000,0.6500]) | ([0.6835,0.7337], [0.3178,0.3680]) | |
([0.5834,0.6334], [0.4183,0.4684]) | ([0.3134,0.3619], [0.6971,0.7473]) | ([0.8000,0.8500], [0.2000,0.2500]) | ([0.3842,0.4339], [0.6188,0.6689]) | |
([0.4836,0.5335], [0.5186,0.5687]) | ([0.7469,0.7980], [0.2551,0.3059]) | ([0.6242,0.6745], [0.3776,0.4279]) | ([0.2000,0.2500], [0.8000,0.8500]) | |
([0.7841,0.7337], [0.2169,0.2674]) | ([0.8000,0.8500], [0.2000,0.2500]) | ([0.5834,0.6334], [0.4183,0.4684]) | ([0.3842,0.4339], [0.6188,0.6689]) | |
([0.6835,0.7337], [0.3178,0.3680]) | ([0.4000,0.4500], [0.6000,0.6500]) | ([0.3669,0.4163], [0.6382,0.6883]) | ([0.3256,0.3750], [0.6787,0.7288]) |
Green Suppliers | ||||
---|---|---|---|---|
([0.7249,0.7757], [0.2767,0.3272]) | ([0.4836,0.5335], [0.5186,0.5687]) | ([0.8779,0.9327], [0.1246,0.1777]) | ([0.1000,0.1500], [0.9000,0.9500]) | |
([0.3842,0.4339], [0.6188,0.6689]) | ([0.6835,0.7337], [0.3178,0.3680]) | ([0.2000,0.2500], [0.8000,0.8500]) | ([0.8779,0.9327], [0.1246,0.1777]) | |
([0.4000,0.4500], [0.6000,0.6500]) | ([0.2279,0.2765], [0.7789,0.8290]) | ([0.6341,0.6869], [0.3807,0.4335]) | ([0.6242,0.6745], [0.3776,0.4279]) | |
([0.3475,0.3968], [0.6581,0.7083]) | ([0.4108,0.4601], [0.5966,0.6470]) | ([0.5242,0.5741], [0.4782,0.5284]) | ([0.7841,0.8347], [0.2169,0.2674]) | |
([0.3000,0.3500], [0.7000,0.7500]) | ([0.6835,0.7337], [0.3178,0.3680]) | ([0.6242,0.6745], [0.3776,0.4279]) | ([0.6835,0.7337], [0.3178,0.3680]) |
Green Suppliers | ||||
---|---|---|---|---|
([0.6607,0.7125], [0.3787,0.4342]) | ([0.5811,0.6316], [0.4300,0.4813]) | ([0.7371,0.8042], [0.2935,0.3551]) | ([0.6518,0.7079], [0.4092,0.4678]) | |
([0.5054,0.5550], [0.5050,0.5557]) | ([0.5765,0.6262], [0.4518,0.5044]) | ([0.7308,0.7877], [0.3130,0.3729]) | ([0.8276,0.8927], [0.1959,0.2595]) | |
([0.4281,0.4776], [0.5769,0.6271]) | ([0.7047,0.7579], [0.3362,0.3936]) | ([0.5867,0.6379], [0.4263,0.4780]) | ([0.4926,0.5404], [0.5504,0.6028]) | |
([0.7182,0.7717], [0.3090,0.3649]) | ([0.6367,0.6910], [0.3996,0.4555]) | ([0.5345,0.5844], [0.4696,0.5199]) | ([0.6050,0.6588], [0.4442,0.5007]) | |
([0.5108,0.5590], [0.5478,0.6016]) | ([0.5378,0.5878], [0.4886,0.5409]) | ([0.5020,0.5511], [0.5209,0.5724]) | ([0.5166,0.5651], [0.5351,0.5886]) |
Green Suppliers | |||||
---|---|---|---|---|---|
([0.6637,0.7223], [0.3775,0.4352]) | 0.6332 | 0.1199 | ([0.6549,0.7108], [0.3876,0.4433]) | 0.6237 | |
([0.7146,0.7814], [0.3287,0.3916]) | 0.6866 | 0.1205 | ([0.6597,0.7156], [0.3959,0.4465]) | 0.6256 | |
([0.5706,0.6222], [0.4715,0.5258]) | 0.5441 | 0.1675 | ([0.5360,0.5867], [0.5022,0.5535]) | 0.5149 | |
([0.6337,0.6875], [0.4024,0.4580]) | 0.6045 | 0.1328 | ([0.6206,0.6737], [0.4164,0.4703]) | 0.5921 | |
([0.5171,0.5660], [0.5242,0.5771]) | 0.4958 | 0.1613 | ([0.5166,0.5655], [0.5258,0.5787]) | 0.4949 |
Green Suppliers | The q-RIVOF Ratio System | The q-RIVOF Reference Point Approach | The q-RIVOF Full Multiplicative Form | The Final Ranking |
---|---|---|---|---|
2 | 1 | 2 | 2 | |
1 | 2 | 1 | 1 | |
4 | 5 | 4 | 4 | |
3 | 3 | 3 | 3 | |
5 | 4 | 5 | 5 |
Criteria | Exp.0 | Exp.1 | Exp.2 | Exp.3 | Exp.4 |
---|---|---|---|---|---|
0.241 | 0.400 | 0.200 | 0.200 | 0.200 | |
0.223 | 0.200 | 0.400 | 0.200 | 0.200 | |
0.220 | 0.200 | 0.200 | 0.400 | 0.200 | |
0.316 | 0.200 | 0.200 | 0.200 | 0.400 |
© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Liu, L.; Cao, W.; Shi, B.; Tang, M. Large-Scale Green Supplier Selection Approach under a Q-Rung Interval-Valued Orthopair Fuzzy Environment. Processes 2019, 7, 573. https://doi.org/10.3390/pr7090573
Liu L, Cao W, Shi B, Tang M. Large-Scale Green Supplier Selection Approach under a Q-Rung Interval-Valued Orthopair Fuzzy Environment. Processes. 2019; 7(9):573. https://doi.org/10.3390/pr7090573
Chicago/Turabian StyleLiu, Limei, Wenzhi Cao, Biao Shi, and Ming Tang. 2019. "Large-Scale Green Supplier Selection Approach under a Q-Rung Interval-Valued Orthopair Fuzzy Environment" Processes 7, no. 9: 573. https://doi.org/10.3390/pr7090573