A hybrid inconsistent sustainable chemical industry evaluation method

Ying Han; Zhenyu Lu; Sheng Chen

doi:10.3934/jimo.2018093

Article Contents

2019, Volume 15, Issue 3: 1225-1239. Doi: 10.3934/jimo.2018093

This issue Previous Article Linear bilevel multiobjective optimization problem: Penalty approach Next Article A smoothing augmented Lagrangian method for nonconvex, nonsmooth constrained programs and its applications to bilevel problems

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
* Corresponding author: Sheng Chen

Received: July 2017

Revised: March 2018

Early access: July 2018

Published: April 2019

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).

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Abstract

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.

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Mathematics Subject Classification: Primary: 62C86, 90B50.

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Figure 1. Flowchart of the proposed method

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Figure 2. Sensitivity analysis of parameter $\nu$

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Figure 3. Comparison of criteria weights

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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 $

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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 $

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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 $

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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 $

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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) $	$(0.7415, 0.7813)$	$(0.285, 0.591)$

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