An extended COPRAS model for multiple attribute group decision making based on single-valued neutrosophic 2-tuple linguistic environment
Abstract
In this article, we develop the COPRAS model to solve the multiple attribute group decision making (MAGDM) under single-valued neutrosophic 2-tuple linguistic sets (SVN2TLSs). Firstly, we introduce the relevant knowledge about SVN2TLSs in a nutshell, such as the definition, the operation laws, a few of fused operators and so on. Then, combine the traditional COPRAS model with SVN2TLNs, and structure as well as elucidate the computing steps of the SVN2TLNCOPRAS pattern. Furthermore, in this article, we propose a method for determining attribute weights in different situations relying on the maximizing deviation method with SVN2TLNs. Last but not least, a numerical example about assessing the safety of construction project has been designed. And for further demonstrating the advantage of the new designed method, we also select a number of existed methods to have comparisons.
First published online 13 January 2021
Keyword : multiple attribute group decision making (MAGDM), single-valued neutrosophic 2-tuple linguistic sets (SVN2TLSs), COPRAS model, construction project
How to Cite
Wei, G., Wu, J., Guo, Y., Wang, J., & Wei, C. (2021). An extended COPRAS model for multiple attribute group decision making based on single-valued neutrosophic 2-tuple linguistic environment. Technological and Economic Development of Economy, 27(2), 353-368. https://doi.org/10.3846/tede.2021.14057
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3
Bekar, E. T., Cakmakci, M., & Kahraman, C. (2016). Fuzzy COPRAS method for performance measurement in total productive maintenance: A comparative analysis. Journal of Business Economics and Management, 17(5), 663–684. https://doi.org/10.3846/16111699.2016.1202314
Chen, J. Q., & Ye, J. (2017). Some Single-valued neutrosophic Dombi weighted aggregation operators for multiple attribute decision-making. Symmetry, 9(6), 82. https://doi.org/10.3390/sym9060082
Fan, C. X., Fan, E., & Ye, J. (2018). The cosine measure of single-valued neutrosophic multisets for multiple attribute decision-making. Symmetry, 10(5), 154. https://doi.org/10.3390/sym10050154
Garg, H. (2016). A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making. International Journal of Intelligent Systems, 31(9), 886–920. https://doi.org/10.1002/int.21809
Garg, H., & Nancy. (2018). Linguistic single-valued neutrosophic prioritized aggregation operators and their applications to multiple-attribute group decision-making. Journal of Ambient Intelligence and Humanized Computing, 9, 1975–1997. https://doi.org/10.1007/s12652-018-0723-5
Gundogdu, F. K., & Kahraman, C. (2019). Spherical fuzzy sets and spherical fuzzy TOPSIS method. Journal of Intelligent & Fuzzy Systems, 36(1), 337–352. https://doi.org/10.3233/JIFS-181401
He, T. T., Wei, G. W., Lu, J. P., Wei, C., & Lin, R. (2019). Pythagorean 2-tuple linguistic Taxonomy method for supplier selection in medical instrument industries. International Journal of Environmental Research and Public Health, 16(23), 4875. https://doi.org/10.3390/ijerph16234875
Herrera, F., & Martinez, L. (2000). A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Transactions on Fuzzy Systems, 8(6), 746–752. https://doi.org/10.1109/91.890332
Ju, D. W., Ju, Y. B., & Wang, A. H. (2018). Multiple attribute group decision making based on Maclaurin symmetric mean operator under single-valued neutrosophic interval 2-tuple linguistic environment. Journal of Intelligent & Fuzzy Systems, 34(4), 2579–2595. https://doi.org/10.3233/JIFS-17496
Liou, J. J. H., Tamosaitiene, J., Zavadskas, E. K., & Tzeng, G. H. (2016). New hybrid COPRAS-G MADM Model for improving and selecting suppliers in green supply chain management. International Journal of Production Research, 54(1), 114–134. https://doi.org/10.1080/00207543.2015.1010747
Mahdiraji, H. A., Arzaghi, S., Stauskis, G., & Zavadskas, E. K. (2018). A hybrid fuzzy BWM-COPRAS method for analyzing key factors of sustainable architecture. Sustainability, 10(5), 1626. https://doi.org/10.3390/su10051626
Matic, B., Jovanovic, S., Das, D. K., Zavadskas, E. K., Stevic, Z., Sremac, S., & Marinkovic, M. (2019). A new hybrid MCDM model: Sustainable supplier selection in a construction company. Symmetry, 11(3), 353. https://doi.org/10.3390/sym11030353
Podvezko, V. (2011). The comparative analysis of MCDA methods SAW and COPRAS. Inzinerine Ekonomika-Engineering Economics, 22(2), 134–146. https://doi.org/10.5755/j01.ee.22.2.310
Roy, J., Sharma, H. K., Kar, S., Zavadskas, E. K., & Saparauskas, J. (2019). An extended COPRAS model for multi-criteria decision-making problems and its application in web-based hotel evaluation and selection. Economic Research-Ekonomska Istrazivanja, 32(1), 219–253. https://doi.org/10.1080/1331677X.2018.1543054
Sahin, R., & Liu, P. D. (2016). Maximizing deviation method for neutrosophic multiple attribute decision making with incomplete weight information. Neural Computing & Applications, 27, 2017–2029. https://doi.org/10.1007/s00521-015-1995-8
Smarandache, F. (1999). A unifying field in logics. Neutrosophy: Neutrosophic probability, set and logic. American Research Press.
Wang, H., Smarandache, F., Zhang, Y. Q., & Sunderraman, R. (2010). Single valued neutrosophic sets. Multispace Multistruct, 4, 410–413.
Wang, J., Gao, H., & Lu, M. (2019a). Approaches to strategic supplier selection under interval neutrosophic environment. Journal of Intelligent & Fuzzy Systems, 37(2), 1707–1730. https://doi.org/10.3233/JIFS-179235
Wang, J., Wei, G. W., & Lu, M. (2018a). TODIM method for multiple attribute group decision making under 2-tuple linguistic neutrosophic environment. Symmetry, 10(10), 486. https://doi.org/10.3390/sym10100486
Wang, J., Wei, G. W., Wei, C., & Wu, J. (2020). Maximizing deviation method for multiple attribute decision making under q-rung orthopair fuzzy environment. Defence Technology, 16(5), 1073–1087. https://doi.org/10.1016/j.dt.2019.11.007
Wang, J., Wei, G. W., & Wei, Y. (2018b). Models for green supplier selection with some 2-tuple linguistic neutrosophic number Bonferroni mean operators. Symmetry, 10(5), 131. https://doi.org/10.3390/sym10050131
Wang, L., Zhang, H. Y., Wang, J. Q., & Li, L. (2018c). Picture fuzzy normalized projection-based VIKOR method for the risk evaluation of construction project. Applied Soft Computing, 64, 216–226. https://doi.org/10.1016/j.asoc.2017.12.014
Wang, P., Wang, J., & Wei, G. W. (2019b). EDAS method for multiple criteria group decision making under 2-tuple linguistic neutrosophic environment. Journal of Intelligent & Fuzzy Systems, 37(2), 1597–1608. https://doi.org/10.3233/JIFS-179223
Wang, Y. M. (1998). Using the method of maximizing deviations to make decision for multi-indices. System Engineering and Electronics, 7, 24–26.
Wei, G. W., Wang, J., Lu, M., Wu, J., & Wei, C. (2019a). Similarity measures of spherical fuzzy sets based on cosine function and their applications. IEEE Access, 7, 159069–159080. https://doi.org/10.1109/ACCESS.2019.2949296
Wei, G. W., Wu, J., Wei, C., Wang, J., & Lu, J. P. (2019b). Models for MADM with 2-tuple linguistic neutrosophic Dombi Bonferroni mean operators. IEEE Access, 7, 108878–108905. https://doi.org/10.1109/ACCESS.2019.2930324
Wu, L. P., Gao, H., & Wei, C. (2019). VIKOR method for financing risk assessment of rural tourism projects under interval-valued intuitionistic fuzzy environment. Journal of Intelligent & Fuzzy Systems, 37(2), 2001–2008. https://doi.org/10.3233/JIFS-179262
Wu, L. P., Wei, G. W., Wu, J., & Wei, C. (2020). Some interval-valued intuitionistic fuzzy Dombi Heronian mean operators and their application for evaluating the ecological value of forest ecological tourism demonstration areas. International Journal of Environmental Research and Public Health, 17(3), 829. https://doi.org/10.3390/ijerph17030829
Wu, Q., Wu, P., Zhou, L. G., Chen, H. Y., & Guan, X. J. (2018). Some new Hamacher aggregation operators under single-valued neutrosophic 2-tuple linguistic environment and their applications to multi-attribute group decision making. Computers & Industrial Engineering, 116, 144–162. https://doi.org/10.1016/j.cie.2017.12.024
Ye, J. (2014). Single valued neutrosophic cross-entropy for multicriteria decision making problems. Applied Mathematical Modelling, 38(3), 1170–1175. https://doi.org/10.1016/j.apm.2013.07.020
Yin, F. L., Lu, L., Chai, J. P., & Yang, Y. B. (2016). Combination weighting method based on maximizing deviations and normalized constraint condition. International Journal of Security and Its Applications, 10(2), 39–50. https://doi.org/10.14257/ijsia.2016.10.2.04
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zavadskas, E. K., Kaklauskas, A., & Kvederyte, N. (2001). Multivariant design and multiple criteria analysis of a building life cycle. Informatica, 12(1), 169–188.
Zavadskas, E. K., Kaklauskas, A., & Sarka, V. (1994). The new method of multi-criteria complex proportional assessment of projects. Technological and Economic Development of Economy, 3, 131–139.
Zhang, X. L., & Xu, Z. S. (2014). Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. International Journal of Intelligent Systems, 29, 1061–1078. https://doi.org/10.1002/int.21676
Bekar, E. T., Cakmakci, M., & Kahraman, C. (2016). Fuzzy COPRAS method for performance measurement in total productive maintenance: A comparative analysis. Journal of Business Economics and Management, 17(5), 663–684. https://doi.org/10.3846/16111699.2016.1202314
Chen, J. Q., & Ye, J. (2017). Some Single-valued neutrosophic Dombi weighted aggregation operators for multiple attribute decision-making. Symmetry, 9(6), 82. https://doi.org/10.3390/sym9060082
Fan, C. X., Fan, E., & Ye, J. (2018). The cosine measure of single-valued neutrosophic multisets for multiple attribute decision-making. Symmetry, 10(5), 154. https://doi.org/10.3390/sym10050154
Garg, H. (2016). A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making. International Journal of Intelligent Systems, 31(9), 886–920. https://doi.org/10.1002/int.21809
Garg, H., & Nancy. (2018). Linguistic single-valued neutrosophic prioritized aggregation operators and their applications to multiple-attribute group decision-making. Journal of Ambient Intelligence and Humanized Computing, 9, 1975–1997. https://doi.org/10.1007/s12652-018-0723-5
Gundogdu, F. K., & Kahraman, C. (2019). Spherical fuzzy sets and spherical fuzzy TOPSIS method. Journal of Intelligent & Fuzzy Systems, 36(1), 337–352. https://doi.org/10.3233/JIFS-181401
He, T. T., Wei, G. W., Lu, J. P., Wei, C., & Lin, R. (2019). Pythagorean 2-tuple linguistic Taxonomy method for supplier selection in medical instrument industries. International Journal of Environmental Research and Public Health, 16(23), 4875. https://doi.org/10.3390/ijerph16234875
Herrera, F., & Martinez, L. (2000). A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Transactions on Fuzzy Systems, 8(6), 746–752. https://doi.org/10.1109/91.890332
Ju, D. W., Ju, Y. B., & Wang, A. H. (2018). Multiple attribute group decision making based on Maclaurin symmetric mean operator under single-valued neutrosophic interval 2-tuple linguistic environment. Journal of Intelligent & Fuzzy Systems, 34(4), 2579–2595. https://doi.org/10.3233/JIFS-17496
Liou, J. J. H., Tamosaitiene, J., Zavadskas, E. K., & Tzeng, G. H. (2016). New hybrid COPRAS-G MADM Model for improving and selecting suppliers in green supply chain management. International Journal of Production Research, 54(1), 114–134. https://doi.org/10.1080/00207543.2015.1010747
Mahdiraji, H. A., Arzaghi, S., Stauskis, G., & Zavadskas, E. K. (2018). A hybrid fuzzy BWM-COPRAS method for analyzing key factors of sustainable architecture. Sustainability, 10(5), 1626. https://doi.org/10.3390/su10051626
Matic, B., Jovanovic, S., Das, D. K., Zavadskas, E. K., Stevic, Z., Sremac, S., & Marinkovic, M. (2019). A new hybrid MCDM model: Sustainable supplier selection in a construction company. Symmetry, 11(3), 353. https://doi.org/10.3390/sym11030353
Podvezko, V. (2011). The comparative analysis of MCDA methods SAW and COPRAS. Inzinerine Ekonomika-Engineering Economics, 22(2), 134–146. https://doi.org/10.5755/j01.ee.22.2.310
Roy, J., Sharma, H. K., Kar, S., Zavadskas, E. K., & Saparauskas, J. (2019). An extended COPRAS model for multi-criteria decision-making problems and its application in web-based hotel evaluation and selection. Economic Research-Ekonomska Istrazivanja, 32(1), 219–253. https://doi.org/10.1080/1331677X.2018.1543054
Sahin, R., & Liu, P. D. (2016). Maximizing deviation method for neutrosophic multiple attribute decision making with incomplete weight information. Neural Computing & Applications, 27, 2017–2029. https://doi.org/10.1007/s00521-015-1995-8
Smarandache, F. (1999). A unifying field in logics. Neutrosophy: Neutrosophic probability, set and logic. American Research Press.
Wang, H., Smarandache, F., Zhang, Y. Q., & Sunderraman, R. (2010). Single valued neutrosophic sets. Multispace Multistruct, 4, 410–413.
Wang, J., Gao, H., & Lu, M. (2019a). Approaches to strategic supplier selection under interval neutrosophic environment. Journal of Intelligent & Fuzzy Systems, 37(2), 1707–1730. https://doi.org/10.3233/JIFS-179235
Wang, J., Wei, G. W., & Lu, M. (2018a). TODIM method for multiple attribute group decision making under 2-tuple linguistic neutrosophic environment. Symmetry, 10(10), 486. https://doi.org/10.3390/sym10100486
Wang, J., Wei, G. W., Wei, C., & Wu, J. (2020). Maximizing deviation method for multiple attribute decision making under q-rung orthopair fuzzy environment. Defence Technology, 16(5), 1073–1087. https://doi.org/10.1016/j.dt.2019.11.007
Wang, J., Wei, G. W., & Wei, Y. (2018b). Models for green supplier selection with some 2-tuple linguistic neutrosophic number Bonferroni mean operators. Symmetry, 10(5), 131. https://doi.org/10.3390/sym10050131
Wang, L., Zhang, H. Y., Wang, J. Q., & Li, L. (2018c). Picture fuzzy normalized projection-based VIKOR method for the risk evaluation of construction project. Applied Soft Computing, 64, 216–226. https://doi.org/10.1016/j.asoc.2017.12.014
Wang, P., Wang, J., & Wei, G. W. (2019b). EDAS method for multiple criteria group decision making under 2-tuple linguistic neutrosophic environment. Journal of Intelligent & Fuzzy Systems, 37(2), 1597–1608. https://doi.org/10.3233/JIFS-179223
Wang, Y. M. (1998). Using the method of maximizing deviations to make decision for multi-indices. System Engineering and Electronics, 7, 24–26.
Wei, G. W., Wang, J., Lu, M., Wu, J., & Wei, C. (2019a). Similarity measures of spherical fuzzy sets based on cosine function and their applications. IEEE Access, 7, 159069–159080. https://doi.org/10.1109/ACCESS.2019.2949296
Wei, G. W., Wu, J., Wei, C., Wang, J., & Lu, J. P. (2019b). Models for MADM with 2-tuple linguistic neutrosophic Dombi Bonferroni mean operators. IEEE Access, 7, 108878–108905. https://doi.org/10.1109/ACCESS.2019.2930324
Wu, L. P., Gao, H., & Wei, C. (2019). VIKOR method for financing risk assessment of rural tourism projects under interval-valued intuitionistic fuzzy environment. Journal of Intelligent & Fuzzy Systems, 37(2), 2001–2008. https://doi.org/10.3233/JIFS-179262
Wu, L. P., Wei, G. W., Wu, J., & Wei, C. (2020). Some interval-valued intuitionistic fuzzy Dombi Heronian mean operators and their application for evaluating the ecological value of forest ecological tourism demonstration areas. International Journal of Environmental Research and Public Health, 17(3), 829. https://doi.org/10.3390/ijerph17030829
Wu, Q., Wu, P., Zhou, L. G., Chen, H. Y., & Guan, X. J. (2018). Some new Hamacher aggregation operators under single-valued neutrosophic 2-tuple linguistic environment and their applications to multi-attribute group decision making. Computers & Industrial Engineering, 116, 144–162. https://doi.org/10.1016/j.cie.2017.12.024
Ye, J. (2014). Single valued neutrosophic cross-entropy for multicriteria decision making problems. Applied Mathematical Modelling, 38(3), 1170–1175. https://doi.org/10.1016/j.apm.2013.07.020
Yin, F. L., Lu, L., Chai, J. P., & Yang, Y. B. (2016). Combination weighting method based on maximizing deviations and normalized constraint condition. International Journal of Security and Its Applications, 10(2), 39–50. https://doi.org/10.14257/ijsia.2016.10.2.04
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zavadskas, E. K., Kaklauskas, A., & Kvederyte, N. (2001). Multivariant design and multiple criteria analysis of a building life cycle. Informatica, 12(1), 169–188.
Zavadskas, E. K., Kaklauskas, A., & Sarka, V. (1994). The new method of multi-criteria complex proportional assessment of projects. Technological and Economic Development of Economy, 3, 131–139.
Zhang, X. L., & Xu, Z. S. (2014). Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. International Journal of Intelligent Systems, 29, 1061–1078. https://doi.org/10.1002/int.21676