Abstract
The location of the electric vehicle charging station (EVCS) is the important link in the construction of the EVCS. The optimal location of the electric vehicle directly affects the operating efficiency of the charging station and the satisfaction of the electric vehicle user, site selection play an important part throughout whole life cycle, which is deemed to be multiple attribute group decision making (MAGDM) issue involving many experts and many conflicting attributes. In practical MAGDM issues, the information of uncertain and fuzzy cognitive decision is well-depicted by uncertain linguistic term sets (ULTSs). These ULTSs could be simply shifted into the probabilistic uncertain linguistic sets (PULTSs). In such paper, we design some novel probabilistic uncertain linguistic weighted Dice similarity measures (PULWDSM) and the probabilistic uncertain linguistic weighted generalized Dice similarity measures (PULWGDSM). Subsequently, the PULWGDSM-based MAGDM methods are presented under PULTSs. In the end, a practical case which concerns about the location planning of electric vehicle charging stations is offered to demonstrate the proposed PULWGDSM’s applicability and advantages.
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References
Chen, S.M., Han, W.H.: Multiattribute decision making based on nonlinear programming methodology, particle swarm optimization techniques and interval-valued intuitionistic fuzzy values. Inf. Sci. 471, 252–268 (2019)
Wang, J., Lu, J.P., Wei, G.W., Lin, R., Wei, C.: Models for MADM with single-valued neutrosophic 2-tuple linguistic Muirhead mean operators. Mathematics 7, 442 (2019)
Wei, G.W., Wu, J., Wei, C., Wang, J., Lu, J.P.: Models for MADM with 2-tuple linguistic neutrosophic Dombi Bonferroni mean operators. IEEE Access 71, 108878–108905 (2019)
Herrera, F., Martinez, L.: A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans. Fuzzy Syst. 8, 746–752 (2000)
Herrera, F., Martinez, L.: A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decision-making. IEEE Trans. Syst. Man Cybern. B 31, 227–234 (2001)
Rodriguez, R.M., Martinez, L., Herrera, F.: Hesitant fuzzy linguistic term sets for decision making. IEEE Trans. Fuzzy Syst. 20, 109–119 (2012)
Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25, 529–539 (2010)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Inf. Sci. 8, 301–357 (1975)
Wei, G.W.: The generalized Dice similarity measures for multiple attribute decision making with hesitant fuzzy linguistic information. Econ. Res. 32, 1498–1520 (2019)
Pang, Q., Wang, H., Xu, Z.S.: Probabilistic linguistic term sets in multi-attribute group decision making. Inf. Sci. 369, 128–143 (2016)
Zhang, Y.X., Xu, Z.S., Wang, H., Liao, H.C.: Consistency-based risk assessment with probabilistic linguistic preference relation. Appl. Soft Comput. 49, 817–833 (2016)
Liang, D.C., Kobina, A., Quan, W.: Grey relational analysis method for probabilistic linguistic multi-criteria group decision-making based on geometric Bonferroni mean. Int. J. Fuzzy Syst. 20, 2234–2244 (2018)
Lu, J.P., Wei, C., Wu, J., Wei, G.W.: TOPSIS method for probabilistic linguistic MAGDM with entropy weight and its application to supplier selection of new agricultural machinery products. Entropy 21, 953 (2019)
Wei, G.W., Wei, C., Wu, J., Wang, H.J.: Supplier selection of medical consumption products with a probabilistic linguistic MABAC method. Int. J. Environ. Res. Public Health 16, 5082 (2019)
Lin, M.W., Chen, Z.Y., Liao, H.C., Xu, Z.S.: ELECTRE II method to deal with probabilistic linguistic term sets and its application to edge computing. Nonlinear Dyn. 96, 2125–2143 (2019)
Liao, H.C., Jiang, L.S., Lev, B., Fujitac, H.: Novel operations of PLTSs based on the disparity degrees of linguistic terms and their use in designing the probabilistic linguistic ELECTRE III method. Appl. Soft Comput. 80, 450–464 (2019)
Kobina, A., Liang, D.C., He, X.: Probabilistic linguistic power aggregation operators for multi-criteria group decision making. Symmetry Basel 9, 320 (2017)
Wang, J., Wei, G.W., Wei, C., Wei, Y.: Dual Hesitant q-rung orthopair fuzzy Muirhead mean operators in multiple attribute decision making. IEEE Access 7, 67139–67166 (2019)
Wang, P., Wei, G.W., Wang, J., Lin, R., Wei, Y.: Dual Hesitant q-rung orthopair fuzzy Hamacher aggregation operators and their applications in scheme selection of construction project. Symmetry Basel 11, 771 (2019)
Chen, S.X., Wang, J.Q., Wang, T.L.: Cloud-based ERP system selection based on extended probabilistic linguistic MULTIMOORA method and Choquet integral operator. Comput. Appl. Math. 38, 88 (2019)
Cheng, X., Gu, J., Xu, Z.S.: Venture capital group decision-making with interaction under probabilistic linguistic environment. Knowl. Based Syst. 140, 82–91 (2018)
Zhai, Y.L., Xu, Z.S., Liao, H.C.: Probabilistic linguistic vector-term set and its application in group decision making with multi-granular linguistic information. Appl. Soft Comput. 49, 801–816 (2016)
Wang, P., Wang, J., Wei, G.W., Wei, C.: Similarity measures of q-rung orthopair fuzzy sets based on cosine function and their applications. Mathematics 7, 340 (2019)
Dice, L.R.: Measures of the amount of ecologic association between species. Ecology 26, 297–302 (1945)
Jaccard, P.: Distribution de la flore alpine dans le Bassin des Drouces et dans quelques regions voisines. Bull. Soc. Vaud. Sci. Nat. 37, 241–272 (1901)
Salton, G., McGill, M.J.: Introduction to Modern Information Retrieval. McGraw-Hill, New York (1987)
Ye, J.: Vector similarity measures of simplified neutrosophic sets and their application in multicriteria decision making. Int. J. Fuzzy Syst. 16, 204–211 (2014)
Ye, J.: The generalized Dice measures for multiple attribute decision making under simplified neutrosophic environments. J. Intell. Fuzzy Syst. 31, 663–671 (2016)
Ye, J.: Multicriteria decision-making method using the Dice similarity measure between expected intervals of trapezoidal fuzzy numbers. J. Decis. Syst. 21, 307–317 (2012)
Ye, J.: Multicriteria group decision-making method using vector similarity measures for trapezoidal intuitionistic fuzzy numbers. Group Decis. Negot. 21, 519–530 (2012)
Tang, Y., Wen, L.L., Wei, G.W.: Approaches to multiple attribute group decision making based on the generalized Dice similarity measures with intuitionistic fuzzy information. Int. J. Knowl. Based Intell. Eng. Syst. 21, 85–95 (2017)
Wang, J., Gao, H., Wei, G.W.: The generalized Dice similarity measures for Pythagorean fuzzy multiple attribute group decision making. Int. J. Intell. Syst. 34, 1158–1183 (2019)
Wei, G.W., Gao, H.: The generalized Dice similarity measures for picture fuzzy sets and their applications. Informatica 29, 107–124 (2018)
Mahmood, T., Ye, J., Khan, Q.: Vector similarity measures for simplified neutrosophic hesitant fuzzy set and their applications. J. Inequal. Spec. Funct. 7, 176–194 (2016)
Mandal, K., Basu, K.: Improved similarity measure in neutrosophic environment and its application in finding minimum spanning tree. J. Intell. Fuzzy Syst. 31, 1721–1730 (2016)
Xu, Z.S.: Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Inf. Sci. 168, 171–184 (2004)
Lin, M.W., Xu, Z.S., Zhai, Y.L., Yao, Z.Q.: Multi-attribute group decision-making under probabilistic uncertain linguistic environment. J. Oper. Res. Soc. 69, 157–170 (2018)
Xie, W.Y., Ren, Z.L., Xu, Z.S., Wang, H.: The consensus of probabilistic uncertain linguistic preference relations and the application on the virtual reality industry. Knowl. Based Syst. 162, 14–28 (2018)
He, Y., Lei, F., Wei, G.W., Wang, R., Wu, J., Wei, C.: EDAS method for multiple attribute group decision making with probabilistic uncertain linguistic information and its application to green supplier selection. Int. J. Comput. Intell. Syst. 12, 1361–1370 (2019)
Wei, G., Lei, F., Lin, R., Wang, R., Wei, Y., Wu, J., Wei, C.: 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. Econ. Res. 33, 828–846 (2020)
Xu, Z.S.: Deviation measures of linguistic preference relations in group decision making. Omega Int. J. Manag. Sci. 33, 249–254 (2005)
Gou, X.J., Xu, Z.S., Liao, H.C.: Multiple criteria decision making based on Bonferroni means with hesitant fuzzy linguistic information. Soft Comput. 21, 6515–6529 (2017)
Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 (1948)
Deng, X.M., Gao, H.: TODIM method for multiple attribute decision making with 2-tuple linguistic Pythagorean fuzzy information. J. Intell. Fuzzy Syst. 37, 1769–1780 (2019)
Lu, J.P., Wei, C.: TODIM method for performance appraisal on social-integration-based rural reconstruction with interval-valued intuitionistic fuzzy information. J. Intell. Fuzzy Syst. 37, 1731–1740 (2019)
Gao, H., Ran, L.G., Wei, G.W., Wei, C., Wu, J.: VIKOR method for MAGDM based on q-rung interval-valued orthopair fuzzy information and its application to supplier selection of medical consumption products. Int. J. Environ. Res. Public Health 17, 525 (2020)
Yucesan, M., Kahraman, G.: Risk evaluation and prevention in hydropower plant operations: a model based on Pythagorean fuzzy AHP. Energy Policy 126, 343–351 (2019)
He, T., Wei, G., Lu, J., Wu, J., Wei, C., Guo, Y.: A novel EDAS based method for multiple attribute group decision making with pythagorean 2-tuple linguistic information. Technol. Econ. Dev. Econ. 26, 1125–1138 (2020)
He, T., Zhang, S., Wei, G., Wang, R., Wu, J., Wei, C.: CODAS method for 2-tuple linguistic pythagorean fuzzy multiple attribute group decision making and its application to financial management performance assessment. Technol. Econ. Dev. Econ. 26, 920–932 (2020)
Wei, G., Tang, Y., Zhao, M., Lin, R., Wu, J.: Selecting the low-carbon tourism destination: based on Pythagorean fuzzy taxonomy method. Mathematics 8, 832 (2020)
Zavadskas, E.K., Antucheviciene, J., Chatterjee, P.: Multiple-criteria decision-making (MCDM) techniques for business processes information management. Information (2019). https://doi.org/10.3390/books978-3-03897-643-1
Wang, P., Wang, J., Wei, G.W., Wu, J., Wei, C., Wei, Y.: CODAS method for multiple attribute group decision making under 2-tuple linguistic neutrosophic environment. Informatica 31, 161–184 (2020)
Zhang, S., Wei, G., Alsaadi, F.E., Hayat, T., Wei, C., Zhang, Z.: MABAC method for multiple attribute group decision making under picture 2-tuple linguistic environment. Soft Comput. 24, 5819–5829 (2020)
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Appendices
Appendix 1 for Example 1
Let \({\text{PUL}}_{1} \left( p \right) = \left\{ {\left\langle {\left[ {l_{{1}} ,\;l_{{2}} } \right],\;0.{4}} \right\rangle ,\;\left\langle {\left[ {l_{{2}} ,\;l_{{3}} } \right],\;0.{6}} \right\rangle } \right\},\;\left\{ {\left\langle {\left[ {l_{{0}} ,\;l_{{1}} } \right],\;0.{2}} \right\rangle ,\;\left\langle {\left[ {l_{{1}} ,\;l_{{2}} } \right],\;0.{8}} \right\rangle } \right\},\;\left\{ {\left\langle {\left[ {l_{{ - 2}} ,\;l_{{ - 1}} } \right],\;0.{2}} \right\rangle ,\;\left\langle {\left[ {l_{{0}} ,\;l_{{1}} } \right],\;0.{8}} \right\rangle } \right\}\) and \({\text{PUL}}_{2} \left( p \right) = \left\{ {\left\langle {\left[ {l_{{ - 3}} ,\;l_{{ - 2}} } \right],\;0.{8}} \right\rangle ,\;\left\langle {\left[ {l_{{ - 2}} ,\;l_{{ - 1}} } \right],\;0.{2}} \right\rangle } \right\},\;\left\{ {\left\langle {\left[ {l_{{1}} ,\;l_{{2}} } \right],\;0.{6}} \right\rangle ,\;\left\langle {\left[ {l_{{2}} ,\;l_{{3}} } \right],\;0.{4}} \right\rangle } \right\},\;\left\{ {\left\langle {\left[ {l_{{ - 1}} ,\;l_{{1}} } \right],\;0.{7}} \right\rangle ,\;\left\langle {\left[ {l_{{1}} ,\;l_{{2}} } \right],\;0.{3}} \right\rangle } \right\}\) be two sets of normalized PULTSs, let \(\lambda = 0.3\), then according to the Eqs. (13)–(14), we can obtain:
Appendix 2 for Example 2
Let \({\text{PUL}}_{1} \left( p \right) = \left\{ {\left\langle {\left[ {l_{{1}} ,\;l_{{2}} } \right],\;0.{4}} \right\rangle ,\;\left\langle {\left[ {l_{{2}} ,\;l_{{3}} } \right],\;0.{6}} \right\rangle } \right\},\;\left\{ {\left\langle {\left[ {l_{{0}} ,\;l_{{1}} } \right],\;0.{2}} \right\rangle ,\;\left\langle {\left[ {l_{{1}} ,\;l_{{2}} } \right],\;0.{8}} \right\rangle } \right\},\;\left\{ {\left\langle {\left[ {l_{{ - 2}} ,\;l_{{ - 1}} } \right],\;0.{2}} \right\rangle ,\;\left\langle {\left[ {l_{{0}} ,\;l_{{1}} } \right],\;0.{8}} \right\rangle } \right\}\) and \({\text{PUL}}_{2} \left( p \right) = \left\{ {\left\langle {\left[ {l_{{ - 3}} ,\;l_{{ - 2}} } \right],\;0.{8}} \right\rangle ,\;\left\langle {\left[ {l_{{ - 2}} ,\;l_{{ - 1}} } \right],\;0.{2}} \right\rangle } \right\},\;\left\{ {\left\langle {\left[ {l_{{1}} ,\;l_{{2}} } \right],\;0.{6}} \right\rangle ,\;\left\langle {\left[ {l_{{2}} ,\;l_{{3}} } \right],\;0.{4}} \right\rangle } \right\},\;\left\{ {\left\langle {\left[ {l_{{ - 1}} ,\;l_{{1}} } \right],\;0.{7}} \right\rangle ,\;\left\langle {\left[ {l_{{1}} ,\;l_{{2}} } \right],\;0.{3}} \right\rangle } \right\}\) be two sets of normalized PULTSs, the weight values are: \(\omega = \left( {0.2,\;0.5,\;0.3} \right)^{T}\), \(\lambda = 0.3\) then according to the Eqs. (21)–(22), we can get:
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Wei, G., Lin, R., Lu, J. et al. The Generalized Dice Similarity Measures for Probabilistic Uncertain Linguistic MAGDM and Its Application to Location Planning of Electric Vehicle Charging Stations. Int. J. Fuzzy Syst. 24, 933–948 (2022). https://doi.org/10.1007/s40815-021-01084-z
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DOI: https://doi.org/10.1007/s40815-021-01084-z