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A hybrid inconsistent sustainable chemical industry evaluation method

  • * Corresponding author: Sheng Chen

    * Corresponding author: Sheng Chen
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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  • 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.

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


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  • 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 $
     | Show Table
    DownLoad: CSV

    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 $
     | Show Table
    DownLoad: CSV

    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 $
     | Show Table
    DownLoad: CSV

    Table 4.  The comprehensive BLFM

    $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 $
     | Show Table
    DownLoad: CSV

    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)$
     | Show Table
    DownLoad: CSV
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