doi: 10.3934/jimo.2018093

A hybrid inconsistent sustainable chemical industry evaluation method

1. 

B-DAT & CICAEET, Nanjing University of Information Science and Technology, Jiangsu, Nanjing 210044, China

2. 

School of Electronic & Information Engineering, Nanjing University of Information Science and Technology, Jiangsu, Nanjing 210044, China

* Corresponding author: Sheng Chen

Received  July 2017 Revised  March 2018 Published  July 2018

Fund Project: The first author is supported by the National Natural Science Foundation of China (61503191, 71503136), the Natural Science Foundation of Jiangsu Province, China (BK20150933), and the Joint Key Grant of National Natural Science Foundation of China and Zhejiang Province (U1509217)

Depletion of energy and environment pollution problems are the unprecedented challenges faced by the conventional chemical industry in China. The ever-growing awareness of energy and environment protection makes sustainable development increasingly play the crucial role in China's chemical industry. Most existing methods about chemical industry evaluation are economic-oriented, which neglect the environmental and social issues, especially conflicts among them. This paper develops a novel hybrid multiple criteria decision making framework under bipolar linguistic fuzzy environment based on VIKOR and fuzzy cognitive map to evaluate sustainable chemical industry. The new method captures the characteristics of uncertainty, inconsistency and complexity in the evaluation process of sustainable chemical industry. Meanwhile, combination of fuzzy cognitive map technique makes the new method consider not only the importance but also the interrelations about criteria and obtain better insight into sustainable chemical industry evaluation. A case study and comparison analysis with existing methods reflect the new proposed framework is more suitable to the needs of environment and energy protection in the sustainable chemical industry.

Citation: Ying Han, Zhenyu Lu, Sheng Chen. A hybrid inconsistent sustainable chemical industry evaluation method. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2018093
References:
[1]

G. Y. BaoX. L. LianM. He and L. L. Wang, Improved two-tuple linguistic representation model based on new linguistic evaluation scale, Control and Decision, 25 (2010), 780-784.

[2]

H. BustinceE. BarrenecheaM. PagolaJ. FernandezZ. S. XuB. BedregalJ. MonteroH. HagraF. Herrera and B. De Baets, A historical account of types of fuzzy sets and their relationships, IEEE Transactions on Fuzzy Systems, 24 (2016), 179-194.

[3]

F. T. S. ChanN. LiS. H. Chung and M. Saadat, Management of sustainable manufacturing systems-a review on mathematical problems, International Journal of Production Research, 55 (2017), 1210-1225. doi: 10.1080/00207543.2016.1229067.

[4]

M. DelgadoJ. L. Verdegay and M. A. Vila, Linguistic decision making models, International Journal of Intelligent Systems, 7 (1992), 479-492. doi: 10.1002/int.4550070507.

[5]

Global Reporting Initiative (GRI), (2010), http://www.globalreporting.org.

[6]

Y. M. HanZ. Q. GengQ. X. Zhu and Y. X. Qu, Energy efficiency analysis method based on fuzzy DEA cross-model for ethylene production systems in chemical industry, Energy, 83 (2015), 685-695. doi: 10.1016/j.energy.2015.02.078.

[7]

Y. Han, C. C. Lim and S. Chen, Triple I fuzzy modus tollness method with inconsistent bipolarity information, Journal of Intelligent & Fuzzy Systems, preprint, 32 (2017), 4299-4309

[8]

Y. HanQ. Luo and S. Chen, Hesitant bipolar fuzzy set and its application in decision making, 2016 Frontiers in Artificial Intelligence and Applications, 293 (2016), 115-121.

[9]

Y. HanP. Shi and S. Chen, Bipolar-valued rough fuzzy set and its applications to decision information system, IEEE Transactions on Fuzzy Systems, 23 (2015), 2358-2370. doi: 10.1109/TFUZZ.2015.2423707.

[10]

A. Hatami-MarbiniJ. A. PerT. Madjid and P. Khoshnevis, A flexible cross-efficiency fuzzy data envelopment analysis model for sustainable sourcing, Journal of Cleaner Production, 142 (2017), 2761-2779. doi: 10.1016/j.jclepro.2016.10.192.

[11]

D. K. Iakovidis and E. Papageorgiou, Intuitionisitc fuzzy cognitive maps for medical decision making, IEEE Transactions on Information Technology in Biomedicine, 15 (2011), 100-107.

[12]

B. Koskom, Fuzzy cognitive maps, International Journal on Man-Machined Studies, 24 (1986), 65-75.

[13]

N. N. Li and H. R. Zhao, Performance evaluation of eco-industrial thermal power plants by using fuzzy GRA-VIKOR and combination weighting techniques, Journal of Cleaner Production, 135 (2016), 169-183. doi: 10.1016/j.jclepro.2016.06.113.

[14]

S. MeiY. F. ZhuX. G. QiuX. ZhouZ. H. ZuA. V. Boukhanovsky and P. M. A. Sloot, Individual decision making can drive epidemics: A fuzzy cognitive map study, IEEE Transactions on Fuzzy Systems, 22 (2014), 264-273. doi: 10.1109/TFUZZ.2013.2251638.

[15]

M. MendoncaB. AngelicoaL. V. R. Arruda and F. Neves Jr., A dynamic fuzzy cognitive map applied to chemical process supervision, Engineering Applications of Artificial Intelligence, 26 (2013), 1199-1210. doi: 10.1016/j.engappai.2012.11.007.

[16]

E. I. Papageorgiou and J. L. Salmeron, Learning fuzzy grey cognitive maps using nonlinear Hebbian-based approach, International Journal of Approximate Reasoning, 53 (2012), 54-65. doi: 10.1016/j.ijar.2011.09.006.

[17]

E. I. PapageorgiouJ. L. Salmeron and P. P. Groumpos, Fuzzy cognitive map learning based on nonlinear Hebbian rule, IN: AI 2003: Advances in Artificial Intelligence, LNCS, 2903 (2003), 256-268. doi: 10.1007/978-3-540-24581-0_22.

[18]

W. Pedrycz and W. Homenda, From fuzzy cognitive maps to granular cognitive maps, Computational Collective Intelligence. Technologies and Applications, (2012), 185-193. doi: 10.1007/978-3-642-34630-9_19.

[19]

M. ShahbazS. Khan and M. I. Tahir, The dynamic links between energy consumption, economic growth, financial development and trade in China: fresh evidence from multivariate framework analysis, Energy Economy, 40 (2013), 8-21. doi: 10.1016/j.eneco.2013.06.006.

[20]

J. Q. WangJ. T. Wu and J. Wang, Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems, Information Sciences, 288 (2014), 55-72. doi: 10.1016/j.ins.2014.07.034.

[21]

G. XieW. Yue and S. Wang, Optimal selection of cleaner products in a green supply chain with risk aversion, Journal of Industrial & Management Optimization, 11 (2015), 515-528. doi: 10.3934/jimo.2015.11.515.

[22]

J. Xu and P. Wei, Production-distribution planning of construction supply chain management under fuzzy random environment for large-scale construction projects, Journal of Industrial & Management Optimization, 9 (2013), 31-56. doi: 10.3934/jimo.2013.9.31.

[23]

R. R. Yager, The power average operator, IEEE Transactions on Systems, Man and Cybernetics-Part A: Systems and Humans, 31 (2001), 724-731. doi: 10.1109/3468.983429.

[24]

W. R. Zhang, Bipolar fuzzy sets and relations: A computational framework for cognitive modeling and multiagent decision analysis, Proceedings of IEEE Conf., (1994), 305-309.

[25]

J. ZhaoJ. Wei and Y. Li, Pricing and remanufacturing decisions for two substitutable products with a common retailer, Journal of Industrial & Management Optimization, 13 (2017), 31-56. doi: 10.3934/jimo.2016065.

show all references

References:
[1]

G. Y. BaoX. L. LianM. He and L. L. Wang, Improved two-tuple linguistic representation model based on new linguistic evaluation scale, Control and Decision, 25 (2010), 780-784.

[2]

H. BustinceE. BarrenecheaM. PagolaJ. FernandezZ. S. XuB. BedregalJ. MonteroH. HagraF. Herrera and B. De Baets, A historical account of types of fuzzy sets and their relationships, IEEE Transactions on Fuzzy Systems, 24 (2016), 179-194.

[3]

F. T. S. ChanN. LiS. H. Chung and M. Saadat, Management of sustainable manufacturing systems-a review on mathematical problems, International Journal of Production Research, 55 (2017), 1210-1225. doi: 10.1080/00207543.2016.1229067.

[4]

M. DelgadoJ. L. Verdegay and M. A. Vila, Linguistic decision making models, International Journal of Intelligent Systems, 7 (1992), 479-492. doi: 10.1002/int.4550070507.

[5]

Global Reporting Initiative (GRI), (2010), http://www.globalreporting.org.

[6]

Y. M. HanZ. Q. GengQ. X. Zhu and Y. X. Qu, Energy efficiency analysis method based on fuzzy DEA cross-model for ethylene production systems in chemical industry, Energy, 83 (2015), 685-695. doi: 10.1016/j.energy.2015.02.078.

[7]

Y. Han, C. C. Lim and S. Chen, Triple I fuzzy modus tollness method with inconsistent bipolarity information, Journal of Intelligent & Fuzzy Systems, preprint, 32 (2017), 4299-4309

[8]

Y. HanQ. Luo and S. Chen, Hesitant bipolar fuzzy set and its application in decision making, 2016 Frontiers in Artificial Intelligence and Applications, 293 (2016), 115-121.

[9]

Y. HanP. Shi and S. Chen, Bipolar-valued rough fuzzy set and its applications to decision information system, IEEE Transactions on Fuzzy Systems, 23 (2015), 2358-2370. doi: 10.1109/TFUZZ.2015.2423707.

[10]

A. Hatami-MarbiniJ. A. PerT. Madjid and P. Khoshnevis, A flexible cross-efficiency fuzzy data envelopment analysis model for sustainable sourcing, Journal of Cleaner Production, 142 (2017), 2761-2779. doi: 10.1016/j.jclepro.2016.10.192.

[11]

D. K. Iakovidis and E. Papageorgiou, Intuitionisitc fuzzy cognitive maps for medical decision making, IEEE Transactions on Information Technology in Biomedicine, 15 (2011), 100-107.

[12]

B. Koskom, Fuzzy cognitive maps, International Journal on Man-Machined Studies, 24 (1986), 65-75.

[13]

N. N. Li and H. R. Zhao, Performance evaluation of eco-industrial thermal power plants by using fuzzy GRA-VIKOR and combination weighting techniques, Journal of Cleaner Production, 135 (2016), 169-183. doi: 10.1016/j.jclepro.2016.06.113.

[14]

S. MeiY. F. ZhuX. G. QiuX. ZhouZ. H. ZuA. V. Boukhanovsky and P. M. A. Sloot, Individual decision making can drive epidemics: A fuzzy cognitive map study, IEEE Transactions on Fuzzy Systems, 22 (2014), 264-273. doi: 10.1109/TFUZZ.2013.2251638.

[15]

M. MendoncaB. AngelicoaL. V. R. Arruda and F. Neves Jr., A dynamic fuzzy cognitive map applied to chemical process supervision, Engineering Applications of Artificial Intelligence, 26 (2013), 1199-1210. doi: 10.1016/j.engappai.2012.11.007.

[16]

E. I. Papageorgiou and J. L. Salmeron, Learning fuzzy grey cognitive maps using nonlinear Hebbian-based approach, International Journal of Approximate Reasoning, 53 (2012), 54-65. doi: 10.1016/j.ijar.2011.09.006.

[17]

E. I. PapageorgiouJ. L. Salmeron and P. P. Groumpos, Fuzzy cognitive map learning based on nonlinear Hebbian rule, IN: AI 2003: Advances in Artificial Intelligence, LNCS, 2903 (2003), 256-268. doi: 10.1007/978-3-540-24581-0_22.

[18]

W. Pedrycz and W. Homenda, From fuzzy cognitive maps to granular cognitive maps, Computational Collective Intelligence. Technologies and Applications, (2012), 185-193. doi: 10.1007/978-3-642-34630-9_19.

[19]

M. ShahbazS. Khan and M. I. Tahir, The dynamic links between energy consumption, economic growth, financial development and trade in China: fresh evidence from multivariate framework analysis, Energy Economy, 40 (2013), 8-21. doi: 10.1016/j.eneco.2013.06.006.

[20]

J. Q. WangJ. T. Wu and J. Wang, Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems, Information Sciences, 288 (2014), 55-72. doi: 10.1016/j.ins.2014.07.034.

[21]

G. XieW. Yue and S. Wang, Optimal selection of cleaner products in a green supply chain with risk aversion, Journal of Industrial & Management Optimization, 11 (2015), 515-528. doi: 10.3934/jimo.2015.11.515.

[22]

J. Xu and P. Wei, Production-distribution planning of construction supply chain management under fuzzy random environment for large-scale construction projects, Journal of Industrial & Management Optimization, 9 (2013), 31-56. doi: 10.3934/jimo.2013.9.31.

[23]

R. R. Yager, The power average operator, IEEE Transactions on Systems, Man and Cybernetics-Part A: Systems and Humans, 31 (2001), 724-731. doi: 10.1109/3468.983429.

[24]

W. R. Zhang, Bipolar fuzzy sets and relations: A computational framework for cognitive modeling and multiagent decision analysis, Proceedings of IEEE Conf., (1994), 305-309.

[25]

J. ZhaoJ. Wei and Y. Li, Pricing and remanufacturing decisions for two substitutable products with a common retailer, Journal of Industrial & Management Optimization, 13 (2017), 31-56. doi: 10.3934/jimo.2016065.

Figure 1.  Flowchart of the proposed method
Figure 2.  Sensitivity analysis of parameter $\nu$
Figure 3.  Comparison of criteria weights
Table 1.  The BLFM given by the first expert
$c_1$$c_2$$c_3 $
$u_1$$\langle (s^P_5, 0.8), (s^N_{-4}, -0.75)\rangle $$\langle (s^P_5, 0.85), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_5, 0.9), (s^N_{-3}, -0.5)\rangle $
$u_2$$\langle (s^P_3, 0.5), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_4, 0.7), (s^N_{-2}, -0.3)\rangle $$\langle (s^P_3, 0.5), (s^N_{-3}, -0.5)\rangle $
$u_3$$\langle (s^P_4, 0.7), (s^N_{-2}, -0.4)\rangle $$\langle (s^P_5, 0.9), (s^N_{-1}, -0.2)\rangle $$\langle (s^P_4, 0.7), (s^N_{-2}, -0.3)\rangle $
$u_4$$\langle (s^P_3, 0.7), (s^N_{-4}, -0.7)\rangle $$\langle (s^P_3, 0.5), (s^N_{-2}, -0.3)\rangle $$\langle (s^P_2, 0.3), (s^N_{-3}, -0.5)\rangle $
$c_4$$c_5$$c_6 $
$u_1$$\langle (s^P_6, 1.0), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_5, 0.8), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_4, 0.7), (s^N_{-3}, -0.5)\rangle $
$u_2$$\langle (s^P_4, 0.7), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_3, 0.5), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_3, 0.5), (s^N_{-3}, -0.5)\rangle $
$u_3$$\langle (s^P_5, 0.8), (s^N_{-1}, -0.1)\rangle $$\langle (s^P_5, 0.9), (s^N_{-2}, -0.25)\rangle $$\langle (s^P_3, 0.5), (s^N_{-2}, -0.3)\rangle $
$u_4$$\langle (s^P_3, 0.5), (s^N_{-4}, -0.6)\rangle $$\langle (s^P_4, 0.6), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_2, 0.3), (s^N_{-4}, -0.7)\rangle $
$c_1$$c_2$$c_3 $
$u_1$$\langle (s^P_5, 0.8), (s^N_{-4}, -0.75)\rangle $$\langle (s^P_5, 0.85), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_5, 0.9), (s^N_{-3}, -0.5)\rangle $
$u_2$$\langle (s^P_3, 0.5), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_4, 0.7), (s^N_{-2}, -0.3)\rangle $$\langle (s^P_3, 0.5), (s^N_{-3}, -0.5)\rangle $
$u_3$$\langle (s^P_4, 0.7), (s^N_{-2}, -0.4)\rangle $$\langle (s^P_5, 0.9), (s^N_{-1}, -0.2)\rangle $$\langle (s^P_4, 0.7), (s^N_{-2}, -0.3)\rangle $
$u_4$$\langle (s^P_3, 0.7), (s^N_{-4}, -0.7)\rangle $$\langle (s^P_3, 0.5), (s^N_{-2}, -0.3)\rangle $$\langle (s^P_2, 0.3), (s^N_{-3}, -0.5)\rangle $
$c_4$$c_5$$c_6 $
$u_1$$\langle (s^P_6, 1.0), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_5, 0.8), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_4, 0.7), (s^N_{-3}, -0.5)\rangle $
$u_2$$\langle (s^P_4, 0.7), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_3, 0.5), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_3, 0.5), (s^N_{-3}, -0.5)\rangle $
$u_3$$\langle (s^P_5, 0.8), (s^N_{-1}, -0.1)\rangle $$\langle (s^P_5, 0.9), (s^N_{-2}, -0.25)\rangle $$\langle (s^P_3, 0.5), (s^N_{-2}, -0.3)\rangle $
$u_4$$\langle (s^P_3, 0.5), (s^N_{-4}, -0.6)\rangle $$\langle (s^P_4, 0.6), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_2, 0.3), (s^N_{-4}, -0.7)\rangle $
Table 2.  The BLFM given by the second expert
$c_1$$c_2$$c_3 $
$u_1$$\langle (s^P_6, 1.0), (s^N_{-4}, -0.7)\rangle $$\langle (s^P_5, 0.9), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_5, 0.8), (s^N_{-3}, -0.5)\rangle $
$u_2$$\langle (s^P_4, 0.7), (s^N_{-2}, -0.35)\rangle $$\langle (s^P_4, 0.7), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_4, 0.75), (s^N_{-3}, -0.5)\rangle $
$u_3$$\langle (s^P_5, 0.85), (s^N_{-2}, -0.3)\rangle $$\langle (s^P_4, 0.8), (sv_{-2}, -0.25)\rangle $$\langle (s^P_5, 0.9), (s^N_{-1}, -0.1)\rangle $
$u_4$$\langle (s^P_2, 0.35), (s^N_{-4}, -0.7)\rangle $$\langle (s^P_4, 0.7), (s^N_{-2}, -0.4)\rangle $$\langle (s^P_2, 0.3), (s^N_{-3}, -0.5)\rangle $
$c_4$$c_5$$c_6 $
$u_1$$\langle (s^P_5, 0.85), (s^N_{-4}, -0.7)\rangle $$\langle (s^P_5, 0.8), (s^N_{-2}, -0.35)\rangle $$\langle (s^P_5, 0.9), (sv_{-3}, -0.5)\rangle $
$u_2$$\langle (s^P_4, 0.7), (s^N_{-4}, -0.75)\rangle $$\langle (s^P_3, 0.5), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_4, 0.75), (s^N_{-3}, -0.5)\rangle $
$u_3$$\langle (s^P_5, 0.8), (s^N_{0}, 0.0)\rangle $$\langle (s^P_5, 0.8), (s^N_{-1}, -0.2)\rangle $$\langle (s^P_5, 0.85), (s^N_{-1}, -0.1)\rangle $
$u_4$$\langle (s^P_4, 0.6), (s^N_{-4}, -0.75)\rangle $$\langle (s^P_4, 0.6), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_4, 0.7), (s^N_{-3}, -0.5)\rangle $
$c_1$$c_2$$c_3 $
$u_1$$\langle (s^P_6, 1.0), (s^N_{-4}, -0.7)\rangle $$\langle (s^P_5, 0.9), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_5, 0.8), (s^N_{-3}, -0.5)\rangle $
$u_2$$\langle (s^P_4, 0.7), (s^N_{-2}, -0.35)\rangle $$\langle (s^P_4, 0.7), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_4, 0.75), (s^N_{-3}, -0.5)\rangle $
$u_3$$\langle (s^P_5, 0.85), (s^N_{-2}, -0.3)\rangle $$\langle (s^P_4, 0.8), (sv_{-2}, -0.25)\rangle $$\langle (s^P_5, 0.9), (s^N_{-1}, -0.1)\rangle $
$u_4$$\langle (s^P_2, 0.35), (s^N_{-4}, -0.7)\rangle $$\langle (s^P_4, 0.7), (s^N_{-2}, -0.4)\rangle $$\langle (s^P_2, 0.3), (s^N_{-3}, -0.5)\rangle $
$c_4$$c_5$$c_6 $
$u_1$$\langle (s^P_5, 0.85), (s^N_{-4}, -0.7)\rangle $$\langle (s^P_5, 0.8), (s^N_{-2}, -0.35)\rangle $$\langle (s^P_5, 0.9), (sv_{-3}, -0.5)\rangle $
$u_2$$\langle (s^P_4, 0.7), (s^N_{-4}, -0.75)\rangle $$\langle (s^P_3, 0.5), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_4, 0.75), (s^N_{-3}, -0.5)\rangle $
$u_3$$\langle (s^P_5, 0.8), (s^N_{0}, 0.0)\rangle $$\langle (s^P_5, 0.8), (s^N_{-1}, -0.2)\rangle $$\langle (s^P_5, 0.85), (s^N_{-1}, -0.1)\rangle $
$u_4$$\langle (s^P_4, 0.6), (s^N_{-4}, -0.75)\rangle $$\langle (s^P_4, 0.6), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_4, 0.7), (s^N_{-3}, -0.5)\rangle $
Table 3.  The BLFM given by the third expert
$c_1$$c_2$$c_3 $
$u_1$$\langle (s^P_5, 0.9), (s^N_{-4}, -0.75)\rangle $$\langle (s^P_6, 1.0), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_5, 0.8), (s^N_{-3}, -0.5)\rangle $
$u_2$$\langle (s^P_5, 0.8), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_3, 0.5), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_4, 0.7), (s^N_{-2}, -0.3)\rangle $
$u_3$$\langle (s_5, 0.8), (s^N_{-1}, -0.1)\rangle $$\langle (s^P_5, 0.85), (s^N_{-1}, -0.2)\rangle $$\langle (s^P_4, 0.8), (s^N_{-2}, -0.3)\rangle $
$u_4$$\langle (s^P_4, 0.7), (s^N_{-4}, -0.6)\rangle $$\langle (s^P_2, 0.35), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_4, 0.8), (s^N_{-3}, -0.5)\rangle $
$c_4$$c_5$$c_6 $
$u_1$$\langle (s^P_4, 0.85), (s^N_{-4}, -0.7)\rangle $$\langle (s^P_5, 0.85), (s^N_{-2}, -0.3)\rangle $$\langle (s^P_6, 1.0), (s^N_{-3}, -0.5)\rangle $
$u_2$$\langle (s^P_3, 0.5), (s^N_{-2}, -0.3)\rangle $$\langle (s^P_4, 0.7), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_5, 0.85), (s^N_{-3}, -0.5)\rangle $
$u_3$$\langle (s^P_4, 0.8), (s^N_{-2}, -0.25)\rangle $$\langle (s^P_5, 0.85), (s^N_{-1}, -0.1)\rangle $$\langle (s^P_5, 0.85), (s^N_{-2}, -0.3)\rangle $
$u_4$$\langle (s^P_3, 0.5), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_3, 0.5), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_3, 0.5), (s^N_{-3}, -0.5)\rangle $
$c_1$$c_2$$c_3 $
$u_1$$\langle (s^P_5, 0.9), (s^N_{-4}, -0.75)\rangle $$\langle (s^P_6, 1.0), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_5, 0.8), (s^N_{-3}, -0.5)\rangle $
$u_2$$\langle (s^P_5, 0.8), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_3, 0.5), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_4, 0.7), (s^N_{-2}, -0.3)\rangle $
$u_3$$\langle (s_5, 0.8), (s^N_{-1}, -0.1)\rangle $$\langle (s^P_5, 0.85), (s^N_{-1}, -0.2)\rangle $$\langle (s^P_4, 0.8), (s^N_{-2}, -0.3)\rangle $
$u_4$$\langle (s^P_4, 0.7), (s^N_{-4}, -0.6)\rangle $$\langle (s^P_2, 0.35), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_4, 0.8), (s^N_{-3}, -0.5)\rangle $
$c_4$$c_5$$c_6 $
$u_1$$\langle (s^P_4, 0.85), (s^N_{-4}, -0.7)\rangle $$\langle (s^P_5, 0.85), (s^N_{-2}, -0.3)\rangle $$\langle (s^P_6, 1.0), (s^N_{-3}, -0.5)\rangle $
$u_2$$\langle (s^P_3, 0.5), (s^N_{-2}, -0.3)\rangle $$\langle (s^P_4, 0.7), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_5, 0.85), (s^N_{-3}, -0.5)\rangle $
$u_3$$\langle (s^P_4, 0.8), (s^N_{-2}, -0.25)\rangle $$\langle (s^P_5, 0.85), (s^N_{-1}, -0.1)\rangle $$\langle (s^P_5, 0.85), (s^N_{-2}, -0.3)\rangle $
$u_4$$\langle (s^P_3, 0.5), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_3, 0.5), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_3, 0.5), (s^N_{-3}, -0.5)\rangle $
Table 4.  The comprehensive BLFM
$c_1$$c_2$
$u_1$$\langle (s^P_{5.5391}, 0.93), (s^N_{-4}, -0.725)\rangle $$\langle (s^P_{5.3343}, 0.92), (s^N_{-3}, -0.5)\rangle $
$u_2$$\langle (s^P_{4.1758}, 0.69), (s^N_{-2.4609}, -0.425)\rangle $$\langle (s^P_{ 3.7315}, 0.64), (s^N_{-2.7733}, -0.46)\rangle $
$u_3$$\langle (s^P_{4.8235 }, 0.805), (s^N_{-1.6657}, -0.26)\rangle $$\langle (s^P_{4.5391 }, 0.835), (s^N_{-1.4609}, -0.225)\rangle $
$u_4$$\langle (s^P_{ 2.7733}, 0.5), (s^N_{-4}, -0.7)\rangle $$\langle (s^P_{3.2267}, 0.555), (s^N_{-2.2685}, -0.41)\rangle $
$c_3$$c_4 $
$u_1$$\langle (s^P_{5}, 0.82), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_{4.9774 }, 0.88), (s^N_{- 3.8235}, -0.66)\rangle $
$u_2$$\langle (s^P_{ 3.8235 }, 0.685), (s^N_{-2.6657}, -0.44)\rangle $$\langle (s^P_{ 3.7315}, 0.64), (s^N_{-3.2267}, -0.565)\rangle $
$u_3$$\langle (s^P_{4.5391 }, 0.83), (s^N_{-1.4609}, -0.2)\rangle $$\langle (s^P_{4.7315}, 0.8), (s^N_{-0.0.6861}, -0.095)\rangle $
$u_4$$\langle (s^P_{2.5617}, 0.45), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_{3.5391}, 0.55), (s^N_{- 3.7315}, -0.645)\rangle $
$c_5$$c_6 $
$u_1$$\langle (s^P_{5}, 0.815), (s^N_{- 2.1765}, -0.365)\rangle $$\langle (s^P_{5.1758}, 0.89), (s^N_{-3}, -0.5)\rangle $
$u_2$$\langle (s^P_{3.3343 }, 0.56), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_{4.1758}, 0.73), (s^N_{-3}, -0.5)\rangle $
$u_3$$\langle (s^P_{5}, 0.835), (s^N_{-1.1765}, -0.18)\rangle $$\langle (s^P_{4.6882}, 0.78), (s^N_{-1.4609}, -0.2)\rangle $
$u_4$$\langle (s^P_{3.7315}, 0.57), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_{ 3.3343}, 0.56), (s^N_{-3.2267}, -0.54)\rangle $
$c_1$$c_2$
$u_1$$\langle (s^P_{5.5391}, 0.93), (s^N_{-4}, -0.725)\rangle $$\langle (s^P_{5.3343}, 0.92), (s^N_{-3}, -0.5)\rangle $
$u_2$$\langle (s^P_{4.1758}, 0.69), (s^N_{-2.4609}, -0.425)\rangle $$\langle (s^P_{ 3.7315}, 0.64), (s^N_{-2.7733}, -0.46)\rangle $
$u_3$$\langle (s^P_{4.8235 }, 0.805), (s^N_{-1.6657}, -0.26)\rangle $$\langle (s^P_{4.5391 }, 0.835), (s^N_{-1.4609}, -0.225)\rangle $
$u_4$$\langle (s^P_{ 2.7733}, 0.5), (s^N_{-4}, -0.7)\rangle $$\langle (s^P_{3.2267}, 0.555), (s^N_{-2.2685}, -0.41)\rangle $
$c_3$$c_4 $
$u_1$$\langle (s^P_{5}, 0.82), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_{4.9774 }, 0.88), (s^N_{- 3.8235}, -0.66)\rangle $
$u_2$$\langle (s^P_{ 3.8235 }, 0.685), (s^N_{-2.6657}, -0.44)\rangle $$\langle (s^P_{ 3.7315}, 0.64), (s^N_{-3.2267}, -0.565)\rangle $
$u_3$$\langle (s^P_{4.5391 }, 0.83), (s^N_{-1.4609}, -0.2)\rangle $$\langle (s^P_{4.7315}, 0.8), (s^N_{-0.0.6861}, -0.095)\rangle $
$u_4$$\langle (s^P_{2.5617}, 0.45), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_{3.5391}, 0.55), (s^N_{- 3.7315}, -0.645)\rangle $
$c_5$$c_6 $
$u_1$$\langle (s^P_{5}, 0.815), (s^N_{- 2.1765}, -0.365)\rangle $$\langle (s^P_{5.1758}, 0.89), (s^N_{-3}, -0.5)\rangle $
$u_2$$\langle (s^P_{3.3343 }, 0.56), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_{4.1758}, 0.73), (s^N_{-3}, -0.5)\rangle $
$u_3$$\langle (s^P_{5}, 0.835), (s^N_{-1.1765}, -0.18)\rangle $$\langle (s^P_{4.6882}, 0.78), (s^N_{-1.4609}, -0.2)\rangle $
$u_4$$\langle (s^P_{3.7315}, 0.57), (s^N_{-3}, -0.5)\rangle $$\langle (s^P_{ 3.3343}, 0.56), (s^N_{-3.2267}, -0.54)\rangle $
Table 5.  The interrelations about criteria
$u_1 \to u_6$$u_2 \to u_6$$ u_4 \to u_6 $$ u_3 \to u_4 $$ u_5 \to u_4$
$y_1$$(0.5, 0.4) $$(0.4, 0.4) $$(0.6, 0.6) $$(0.7, 0.3) $$(0.4, 0.8) $
$y_2$$(0.4, 0.5) $$(0.3, 0.5) $$(0.6, 0.6) $$(0.7, 0.5) $$(0.2, 0.6) $
$y_3$$(0.6, 0.6) $$(0.5, 0.5) $$(0.6, 0.7) $$(0.8, 0.3) $$(0.3, 0.8) $
$\bar{R}^{(0)}$$(0.48, 0.51) $$(0.38, 0.48)$$(0.6, 0.63)$$(0.73, 0.4)$$(0.27, 0.7)$
$\bar{R}^{(15)}$$(0.6465, 0.7227)$$(0.5686, 0.7351) $$(0.524, 0.6958) $$(0.7415, 0.7813)$$(0.285, 0.591)$
$u_1 \to u_6$$u_2 \to u_6$$ u_4 \to u_6 $$ u_3 \to u_4 $$ u_5 \to u_4$
$y_1$$(0.5, 0.4) $$(0.4, 0.4) $$(0.6, 0.6) $$(0.7, 0.3) $$(0.4, 0.8) $
$y_2$$(0.4, 0.5) $$(0.3, 0.5) $$(0.6, 0.6) $$(0.7, 0.5) $$(0.2, 0.6) $
$y_3$$(0.6, 0.6) $$(0.5, 0.5) $$(0.6, 0.7) $$(0.8, 0.3) $$(0.3, 0.8) $
$\bar{R}^{(0)}$$(0.48, 0.51) $$(0.38, 0.48)$$(0.6, 0.63)$$(0.73, 0.4)$$(0.27, 0.7)$
$\bar{R}^{(15)}$$(0.6465, 0.7227)$$(0.5686, 0.7351) $$(0.524, 0.6958) $$(0.7415, 0.7813)$$(0.285, 0.591)$
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