CPT-TODIM method for interval-valued bipolar fuzzy multiple attribute group decision making and application to industrial control security service provider selection
Abstract
In recent years, a series of serious attacks against industrial control system (ICS), such as Stuxnet, Duqu, Flame and Havex, have sounded the alarm for industrial enterprises. For many industrial enterprises, it is a very important part of enterprise management decisions to evaluate ICS security suppliers and choose the appropriate one as a partner. The purpose of this paper is to build the TODIM method based on cumulative prospect theory (CPT-TODIM) to solve multiattribute group decision making problem under interval-valued bipolar fuzzy environment. This extraordinary model not only uses CPT to supplement the traditional TODIM method, but also introduces the entropy weight method to determine the attribute weight so as to avoid the negative influence of subjective weight on the decision result. In addition, in this model, all attribute evaluation information will be interval-valued bipolar fuzzy number (IVBFN) to cope with complex and fuzzy decision environment. Then, the most important part of this paper, we elaborate on the logical structure of the model. What’s more, in the last two sections, we apply this newly constructed model to the selection of ICS security suppliers, and verify the acceptability of this method by sensitivity analysis and comparing with IVBFWA and IVBFWG operator.
First published online 05 July 2021
Keyword : multi-attribute group decision making (MAGDM), interval-valued bipolar fuzzy sets, TODIM, CPT, industrial control security, service provider selection
How to Cite
Zhao, M., Wei, G., Guo, Y., & Chen, X. (2021). CPT-TODIM method for interval-valued bipolar fuzzy multiple attribute group decision making and application to industrial control security service provider selection. Technological and Economic Development of Economy, 27(5), 1186-1206. https://doi.org/10.3846/tede.2021.15044
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87−96. https://doi.org/10.1016/S0165-0114(86)80034-3
Gomes, L., & Rangel, L. A. D. (2009). An application of the TODIM method to the multicriteria rental evaluation of residential properties. European Journal of Operational Research, 193, 204−211. https://doi.org/10.1016/j.ejor.2007.10.046
Guo, J., Yin, J. L., Zhang, L., Lin, Z. F., & Li, X. (2020). Extended TODIM method for CCUS storage site selection under probabilistic hesitant fuzzy environment. Applied Soft Computing, 93, 106381. https://doi.org/10.1016/j.asoc.2020.106381
He, S. F., Pan, X. H., & Wang, Y. M. (2021). A shadowed set-based TODIM method and its application to large-scale group decision making. Information Sciences, 544, 135−154. https://doi.org/10.1016/j.ins.2020.07.028
He, T., Wei, G., Lu, J., Wu, J., Wei, C., & Guo, Y. (2020a). A novel EDAS based method for multiple attribute group decision making with pythagorean 2-tuple linguistic information. Technological and Economic Development of Economy, 26, 1125−1138. https://doi.org/10.3846/tede.2020.12733
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Jana, C., Pal, M., & Wang, J. Q. (2020). Bipolar fuzzy Dombi prioritized aggregation operators in multiple attribute decision making. Soft Computing, 24, 3631−3646. https://doi.org/10.1007/s00500-019-04130-z
Keshavarz Ghorabaee, M., Zavadskas, E. K., Olfat, L., & Turskis, Z. (2015). Multi-criteria inventory classification using a new method of Evaluation Based on Distance from Average Solution (EDAS). Informatica, 26, 435−451. https://doi.org/10.15388/Informatica.2015.57
Keshavarz Ghorabaee, M., Zavadskas, E. K., Turskis, Z., & Antucheviciene, J. (2016). A new combinative distance-based assessment (CODAS) method for multi-criteria decision-making. Economic Computation and Economic Cybernetics Studies and Research, 50, 25−44.
Liu, L., Wu, J., Wei, G., Wei, C., Wang, J., & Wei, Y. (2020). Entropy-based GLDS method for social capital selection of a PPP project with q-rung orthopair fuzzy information. Entropy, 22(4), 414. https://doi.org/10.3390/e22040414
Lu, J. P., He, T. T., Wei, G. W., Wu, J., & Wei, C. (2020). Cumulative prospect theory: performance evaluation of government purchases of home-based elderly-care services using the Pythagorean 2-tuple linguistic TODIM method. International Journal of Environmental Research and Public Health, 17(6), 1939. https://doi.org/10.3390/ijerph17061939
Mishra, A. R., Rani, P., Pardasani, K. R., Mardani, A., Stevic, Z., & Pamucar, D. (2020). A novel entropy and divergence measures with multi-criteria service quality assessment using interval-valued intuitionistic fuzzy TODIM method. Soft Computing, 24, 11641−11661. https://doi.org/10.1007/s00500-019-04627-7
Opricovic, S., & Tzeng, G. H. (2004). Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. European Journal of Operational Research, 156, 445−455. https://doi.org/10.1016/S0377-2217(03)00020-1
Paelinck, J. H. P. (1978). Qualiflex - flexible multiple-criteria method. Economics Letters, 1, 193−197. https://doi.org/10.1016/0165-1765(78)90023-X
Pamucar, D., & Cirovic, G. (2015). The selection of transport and handling resources in logistics centers using Multi-Attributive Border Approximation area Comparison (MABAC). Expert Systems with Applications, 42, 3016−3028. https://doi.org/10.1016/j.eswa.2014.11.057
Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27, 379−423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
Tehrim, S. T., & Riaz, M. (2020). An interval-valued bipolar fuzzy linguistic VIKOR method using connection numbers of SPA theory and its application to decision support system. Journal of Intelligent & Fuzzy Systems, 39, 3931−3948. https://doi.org/10.3233/JIFS-200038
Tian, X., Niu, M., Zhang, W., Li, L., & Herrera-Viedma, E. (2021). A novel TODIM based on Prospect theory to select green supplier with q-rung orthopair fuzzy set. Technological and Economic Development of Economy, 27(2), 284−310. https://doi.org/10.3846/tede.2020.12736
Tian, X. L., Niu, M. L., Ma, J. S., & Xu, Z. S. (2020). A novel TODIM with probabilistic hesitant fuzzy information and its application in green supplier selection. Complexity, 2020, 2540798. https://doi.org/10.1155/2020/2540798
Tian, X. L., Xu, Z. S., & Gu, J. (2019). An extended TODIM based on cumulative prospect theory and its application in venture capital. Informatica, 30, 413−429. https://doi.org/10.15388/Informatica.2019.212
Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5, 297–323. https://doi.org/10.1007/BF00122574
Wang, S., Wei, G., Wu, J., Wei, C., & Guo, Y. (2021). Model for selection of hospital constructions with probabilistic linguistic GRP method. Journal of Intelligent & Fuzzy Systems, 40, 1245−1259. https://doi.org/10.3233/JIFS-201543
Wei, G., Lei, F., Lin, R., Wang, R., Wei, Y., Wu, J., & Wei, C. (2020). Algorithms for probabilistic uncertain linguistic multiple attribute group decision making based on the GRA and CRITIC method: application to location planning of electric vehicle charging stations. Economic Research-Ekonomska Istraživanja, 33(1), 828−846. https://doi.org/10.1080/1331677X.2020.1734851
Wei, G. W., Wei, C., & Gao, H. (2018). Multiple attribute decision making with interval-valued bipolar fuzzy information and their application to emerging technology commercialization evaluation. IEEE Access, 6, 60930−60955. https://doi.org/10.1109/ACCESS.2018.2875261
Wu, X. L., & Liao, H. C. (2019). A consensus-based probabilistic linguistic gained and lost dominance score method. European Journal of Operational Research, 272, 1017−1027. https://doi.org/10.1016/j.ejor.2018.07.044
Xiao, L., Zhang, S., Wei, G., Wu, J., Wei, C., Guo, Y., & Wei, Y. (2020). Green supplier selection in steel industry with intuitionistic fuzzy Taxonomy method. Journal of Intelligent & Fuzzy Systems, 39, 7247−7258. https://doi.org/10.3233/JIFS-200709
Xu, D. S., Wei, X. L., Ding, H., & Bin, H. Q. (2020). A new method based on PROMETHEE and TODIM for multi-attribute decision-making with single-valued neutrosophic sets. Mathematics, 8, 1816. https://doi.org/10.3390/math8101816
Yazdani, M., Zarate, P., Zavadskas, E. K., & Turskis, Z. (2018). A combined compromise solution (CoCoSo) method for multi-criteria decision-making problems. Management Decision, 57, 2501−2519. https://doi.org/10.1108/MD-05-2017-0458
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338−356. https://doi.org/10.1016/S0019-9958(65)90241-X
Zhang, W. R. (1996). NPN fuzzy sets and NPN qualitative algebra: A computational framework for bipolar cognitive modeling and multiagent decision analysis. Ieee Transactions on Systems Man and Cybernetics Part B-Cybernetics, 26, 561−574. https://doi.org/10.1109/3477.517031
Zhao, M., Wei, G., Wei, C., & Wu, J. (2021a). Improved TODIM method for intuitionistic fuzzy MAGDM based on cumulative prospect theory and its application on stock investment selection. International Journal of Machine Learning and Cybernetics, 12, 891−901. https://doi.org/10.1007/s13042-020-01208-1
Zhao, M., Wei, G., Wei, C., Wu, J., & Wei, Y. (2021b). Extended CPT-TODIM method for intervalvalued intuitionistic fuzzy MAGDM and its application to urban ecological risk assessment. Journal of Intelligent & Fuzzy Systems, 40(3), 4091−4106. https://doi.org/10.3233/JIFS-200534
Zhao, M., Wei, G., Wu, J., Guo, Y., & Wei, C. (2021c). TODIM method for multiple attribute group decision making based on cumulative prospect theory with 2‐tuple linguistic neutrosophic sets. International Journal of Intelligent Systems, 36, 1199−1222. https://doi.org/10.1002/int.22338
Arya, V., & Kumar, S. (2020a). A new picture fuzzy information measure based on shannon entropy with applications in opinion polls using extended VIKOR-TODIM approach. Computational & Applied Mathematics, 39, 197. https://doi.org/10.1007/s40314-020-01228-1
Arya, V., & Kumar, S. (2020b). A novel TODIM-VIKOR approach based on entropy and Jensen-Tsalli divergence measure for picture fuzzy sets in a decision-making problem. International Journal of Intelligent Systems, 35, 2140−2180. https://doi.org/10.1002/int.22289
Ashofteh, P. S., Golfam, P., & Loaiciga, H. A. (2020). Evaluation of river water transfer alternatives with the TODIM multi-criteria decision making method. Water Resources Management, 34, 4847−4863. https://doi.org/10.1007/s11269-020-02694-2
Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87−96. https://doi.org/10.1016/S0165-0114(86)80034-3
Gomes, L., & Rangel, L. A. D. (2009). An application of the TODIM method to the multicriteria rental evaluation of residential properties. European Journal of Operational Research, 193, 204−211. https://doi.org/10.1016/j.ejor.2007.10.046
Guo, J., Yin, J. L., Zhang, L., Lin, Z. F., & Li, X. (2020). Extended TODIM method for CCUS storage site selection under probabilistic hesitant fuzzy environment. Applied Soft Computing, 93, 106381. https://doi.org/10.1016/j.asoc.2020.106381
He, S. F., Pan, X. H., & Wang, Y. M. (2021). A shadowed set-based TODIM method and its application to large-scale group decision making. Information Sciences, 544, 135−154. https://doi.org/10.1016/j.ins.2020.07.028
He, T., Wei, G., Lu, J., Wu, J., Wei, C., & Guo, Y. (2020a). A novel EDAS based method for multiple attribute group decision making with pythagorean 2-tuple linguistic information. Technological and Economic Development of Economy, 26, 1125−1138. https://doi.org/10.3846/tede.2020.12733
He, T., Zhang, S., Wei, G., Wang, R., Wu, J., & Wei, C. (2020b). CODAS method for 2-tuple linguistic pythagorean fuzzy multiple attribute group decision making and its application to financial management performance assessment. Technological and Economic Development of Economy, 26, 920−932. https://doi.org/10.3846/tede.2020.11970
Jana, C., Pal, M., & Wang, J. Q. (2020). Bipolar fuzzy Dombi prioritized aggregation operators in multiple attribute decision making. Soft Computing, 24, 3631−3646. https://doi.org/10.1007/s00500-019-04130-z
Keshavarz Ghorabaee, M., Zavadskas, E. K., Olfat, L., & Turskis, Z. (2015). Multi-criteria inventory classification using a new method of Evaluation Based on Distance from Average Solution (EDAS). Informatica, 26, 435−451. https://doi.org/10.15388/Informatica.2015.57
Keshavarz Ghorabaee, M., Zavadskas, E. K., Turskis, Z., & Antucheviciene, J. (2016). A new combinative distance-based assessment (CODAS) method for multi-criteria decision-making. Economic Computation and Economic Cybernetics Studies and Research, 50, 25−44.
Liu, L., Wu, J., Wei, G., Wei, C., Wang, J., & Wei, Y. (2020). Entropy-based GLDS method for social capital selection of a PPP project with q-rung orthopair fuzzy information. Entropy, 22(4), 414. https://doi.org/10.3390/e22040414
Lu, J. P., He, T. T., Wei, G. W., Wu, J., & Wei, C. (2020). Cumulative prospect theory: performance evaluation of government purchases of home-based elderly-care services using the Pythagorean 2-tuple linguistic TODIM method. International Journal of Environmental Research and Public Health, 17(6), 1939. https://doi.org/10.3390/ijerph17061939
Mishra, A. R., Rani, P., Pardasani, K. R., Mardani, A., Stevic, Z., & Pamucar, D. (2020). A novel entropy and divergence measures with multi-criteria service quality assessment using interval-valued intuitionistic fuzzy TODIM method. Soft Computing, 24, 11641−11661. https://doi.org/10.1007/s00500-019-04627-7
Opricovic, S., & Tzeng, G. H. (2004). Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. European Journal of Operational Research, 156, 445−455. https://doi.org/10.1016/S0377-2217(03)00020-1
Paelinck, J. H. P. (1978). Qualiflex - flexible multiple-criteria method. Economics Letters, 1, 193−197. https://doi.org/10.1016/0165-1765(78)90023-X
Pamucar, D., & Cirovic, G. (2015). The selection of transport and handling resources in logistics centers using Multi-Attributive Border Approximation area Comparison (MABAC). Expert Systems with Applications, 42, 3016−3028. https://doi.org/10.1016/j.eswa.2014.11.057
Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27, 379−423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
Tehrim, S. T., & Riaz, M. (2020). An interval-valued bipolar fuzzy linguistic VIKOR method using connection numbers of SPA theory and its application to decision support system. Journal of Intelligent & Fuzzy Systems, 39, 3931−3948. https://doi.org/10.3233/JIFS-200038
Tian, X., Niu, M., Zhang, W., Li, L., & Herrera-Viedma, E. (2021). A novel TODIM based on Prospect theory to select green supplier with q-rung orthopair fuzzy set. Technological and Economic Development of Economy, 27(2), 284−310. https://doi.org/10.3846/tede.2020.12736
Tian, X. L., Niu, M. L., Ma, J. S., & Xu, Z. S. (2020). A novel TODIM with probabilistic hesitant fuzzy information and its application in green supplier selection. Complexity, 2020, 2540798. https://doi.org/10.1155/2020/2540798
Tian, X. L., Xu, Z. S., & Gu, J. (2019). An extended TODIM based on cumulative prospect theory and its application in venture capital. Informatica, 30, 413−429. https://doi.org/10.15388/Informatica.2019.212
Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5, 297–323. https://doi.org/10.1007/BF00122574
Wang, S., Wei, G., Wu, J., Wei, C., & Guo, Y. (2021). Model for selection of hospital constructions with probabilistic linguistic GRP method. Journal of Intelligent & Fuzzy Systems, 40, 1245−1259. https://doi.org/10.3233/JIFS-201543
Wei, G., Lei, F., Lin, R., Wang, R., Wei, Y., Wu, J., & Wei, C. (2020). Algorithms for probabilistic uncertain linguistic multiple attribute group decision making based on the GRA and CRITIC method: application to location planning of electric vehicle charging stations. Economic Research-Ekonomska Istraživanja, 33(1), 828−846. https://doi.org/10.1080/1331677X.2020.1734851
Wei, G. W., Wei, C., & Gao, H. (2018). Multiple attribute decision making with interval-valued bipolar fuzzy information and their application to emerging technology commercialization evaluation. IEEE Access, 6, 60930−60955. https://doi.org/10.1109/ACCESS.2018.2875261
Wu, X. L., & Liao, H. C. (2019). A consensus-based probabilistic linguistic gained and lost dominance score method. European Journal of Operational Research, 272, 1017−1027. https://doi.org/10.1016/j.ejor.2018.07.044
Xiao, L., Zhang, S., Wei, G., Wu, J., Wei, C., Guo, Y., & Wei, Y. (2020). Green supplier selection in steel industry with intuitionistic fuzzy Taxonomy method. Journal of Intelligent & Fuzzy Systems, 39, 7247−7258. https://doi.org/10.3233/JIFS-200709
Xu, D. S., Wei, X. L., Ding, H., & Bin, H. Q. (2020). A new method based on PROMETHEE and TODIM for multi-attribute decision-making with single-valued neutrosophic sets. Mathematics, 8, 1816. https://doi.org/10.3390/math8101816
Yazdani, M., Zarate, P., Zavadskas, E. K., & Turskis, Z. (2018). A combined compromise solution (CoCoSo) method for multi-criteria decision-making problems. Management Decision, 57, 2501−2519. https://doi.org/10.1108/MD-05-2017-0458
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338−356. https://doi.org/10.1016/S0019-9958(65)90241-X
Zhang, W. R. (1996). NPN fuzzy sets and NPN qualitative algebra: A computational framework for bipolar cognitive modeling and multiagent decision analysis. Ieee Transactions on Systems Man and Cybernetics Part B-Cybernetics, 26, 561−574. https://doi.org/10.1109/3477.517031
Zhao, M., Wei, G., Wei, C., & Wu, J. (2021a). Improved TODIM method for intuitionistic fuzzy MAGDM based on cumulative prospect theory and its application on stock investment selection. International Journal of Machine Learning and Cybernetics, 12, 891−901. https://doi.org/10.1007/s13042-020-01208-1
Zhao, M., Wei, G., Wei, C., Wu, J., & Wei, Y. (2021b). Extended CPT-TODIM method for intervalvalued intuitionistic fuzzy MAGDM and its application to urban ecological risk assessment. Journal of Intelligent & Fuzzy Systems, 40(3), 4091−4106. https://doi.org/10.3233/JIFS-200534
Zhao, M., Wei, G., Wu, J., Guo, Y., & Wei, C. (2021c). TODIM method for multiple attribute group decision making based on cumulative prospect theory with 2‐tuple linguistic neutrosophic sets. International Journal of Intelligent Systems, 36, 1199−1222. https://doi.org/10.1002/int.22338