Hesitant fuzzy linguistic DNMA method with cardinal consensus reaching process for shopping mall location selection
Abstract
The hesitant fuzzy linguistic term set is an effective tool to express qualitative evaluations since it is close to human reasoning and expressing habits. In this paper, we propose a multi-expert multi-criterion decision-making method integrating the double normalization-based multi-aggregation (DNMA) method with a cardinal consensus reaching process, where the assessments of alternatives over multiple criteria are expressed as hesitant fuzzy linguistic term sets. To do so, the DNMA method involving double normalizations and three aggregation tools is extended to deal with the hesitant fuzzy linguistic information and derive the ranking of alternatives with respect to each expert. In addition, a cardinal consensus reaching process is introduced to help experts reach an acceptable consensus level. In other words, the soft consensus is considered in the multi-expert multi-criterion decision-making process. Subsequently, an extended Borda rule is developed to aggregate the subordinate ranks and integrated scores of alternatives, and then deduce the comprehensive ranking of alternatives. A case study is given to illustrate the practicability of the proposed method for selecting the optimal geographical location of a larger-scale shopping mall in the new urbanization for a construction investment agency. The proposed method is compared with other ranking methods to illustrate its advantages.
Keyword : multi-expert multi-criterion decision making, hesitant fuzzy linguistic term set, double normalization-based multiple aggregation method, cardinal consensus method, extended Borda rule, shopping mall location selection
How to Cite
Nie, S., Liao, H., Wu, X., Tang, M., & Al-Barakati, A. (2019). Hesitant fuzzy linguistic DNMA method with cardinal consensus reaching process for shopping mall location selection. International Journal of Strategic Property Management, 23(6), 420-434. https://doi.org/10.3846/ijspm.2019.10851
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Canas, S. R. D., Ferreira, F. A. F., & Meidutė-Kavaliauskienė, I. (2015). Setting rents in residential real estate: a methodological proposal using multiple criteria decision analysis. International Journal of Strategic Property Management, 19(4), 368-380. https://doi.org/10.3846/1648715X.2015.1093562
Cheng, E. W. L., Li, H., & Yu, L. (2005). The analytic network process (ANP) approach to location selection: a shopping mall illustration. Construction Innovation, 5(2), 83-97. https://doi.org/10.1108/14714170510815195
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Elevli, B. (2014). Logistics freight center locations decision by using Fuzzy-PROMETHEE. Transport, 29(4), 412-418. https://doi.org/10.3846/16484142.2014.983966
ElSamen, A. A. A., & Hiyasat R. I. (2017). Beyond the random location of shopping malls: a GIS perspective in Amman, Jordan. Journal of Retailing and Consumer Services, 34, 30-37. https://doi.org/10.1016/j.jretconser.2016.09.006
Gundogdu, C. E. (2013). Determination of the most suitable sites for shopping centers in geographical regions with GIS. Research in Logistics & Production, 3(2), 109-122.
Herrera, F., Herrera-Viedma, E., & Verdegay, J. L. (1996). Direct approach processes in group decision making using linguistic OWA operators. Fuzzy Sets and Systems, 79, 175-190. https://doi.org/10.1016/0165-0114(95)00162-X
Herrera-Viedma, E., Martínez, L., Mata, F., & Chiclana, F. (2005). A consensus support systems model for group decision making problems with multigranular linguistic preference relations. IEEE Transactions on Fuzzy Systems, 13(5), 644-658. https://doi.org/10.1109/TFUZZ.2005.856561
Kahraman, C., Engin, O., Kabak, O., & Kaya, I. (2009). Information systems outsourcing decisions using a GDM approach. Engineering Applications of Artificial Intelligence, 22(6), 832841. https://doi.org/10.1016/j.engappai.2008.10.009
Lee, H. S. (2002). Optimal consensus of fuzzy opinions under group decision making environment. Fuzzy Sets and Systems, 132(3), 303-315. https://doi.org/10.1016/S0165-0114(02)00056-8
Li, C. C., Dong, Y. C., Herrera, F., & Herrera-Viedma, E. (2017). Personalized individual semantics in computing with words for supporting linguistic group decision making. An application on consensus reaching. Information Fusion, 33, 29-40. https://doi.org/10.1016/j.inffus.2016.04.005
Liao, H. C., & Wu, X. L. (2019). DNMA: a double normalizationbased multiple aggregation method for multi-expert multicriteria decision making. Omega (in press). https://doi.org/10.1016/j.omega.2019.04.001
Liao, H. C., Qin, R., Gao, C. Y., Wu, X. L., Hafezalkotob, A., & Herrera, F. (2019). Score-HeDLiSF: a score function of hesitant fuzzy linguistic term set based on hesitant degrees and linguistic scale functions: an application to unbalanced hesitant fuzzy linguistic MULTIMOORA. Information Fusion, 48, 39-54. https://doi.org/10.1016/j.inffus.2018.08.006
Liao, H. C., Wu, X. L., Liang, X. D., Xu, J. P., & Herrera, F. (2018). A new hesitant fuzzy linguistic ORESTE method for hybrid multi-criteria decision making. IEEE Transactions on Fuzzy Systems, 26(6), 3793-3807. https://doi.org/10.1109/TFUZZ.2018.2849368
Liao, H. C., Wu, X. L., Mi, X. M., & Herrera, F. (2019). An integrated method for cognitive complex multiple experts multiple criteria decision making based on ELECTRE III with weighted Borda rule. Omega (in press). https://doi.org/10.1016/j.omega.2019.03.010
Liao, H. C., Xu, Z. S., & Zeng, X. J. (2015). Hesitant fuzzy linguistic VIKOR method and its application in qualitative multiple criteria decision making. IEEE Transactions on Fuzzy Systems, 23(5), 1343-1355. https://doi.org/10.1109/TFUZZ.2014.2360556
Liao, H. C., Xu, Z. S., Herrera-Viedma, E., & Herrera, F. (2018). Hesitant fuzzy linguistic term set and its application in decision making: a state-of-the-art survey. International Journal of Fuzzy Systems, 20(12), 1-27. https://doi.org/10.1007/s40815-017-0432-9
Liao, H. C., Xu, Z. S., Zeng, X. J., & Merigó, J. M. (2015). Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets. Knowledge-Based Systems, 76, 127-138. https://doi.org/10.1016/j.knosys.2014.12.009
Liu, Y., Liang, C., Chiclana, F., & Wu, J. (2017). A trust induced recommendation mechanism for reaching consensus in group decision making. Knowledge-Based Systems, 119, 221-231. https://doi.org/10.1016/j.knosys.2016.12.014
Parreiras, R. O., Ekel, P. Y., Martini, J. S. C., & Palhares, R. M. (2010). A flexible consensus scheme for multicriteria group decision making under linguistic assessments. Information Sciences, 180(7), 1075-1089. https://doi.org/10.1016/j.ins.2009.11.046
Perez, I. J., Cabrerizo, F. J., Alonso, S., & Herrera-Viedma, E. (2014). A new consensus model for group decision making problems with non-homogeneous experts. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 44(4), 494-498. https://doi.org/10.1109/TSMC.2013.2259155
Rodríguez, R. M., Martínez, L., & Herrera, F. (2012). Hesitant fuzzy linguistic term sets for decision making. IEEE Transactions on Fuzzy Systems, 20(1), 109-119. https://doi.org/10.1109/TFUZZ.2011.2170076
Ross, A., & Jayaraman, V. (2008). An evaluation of new heuristics for the location of cross-docks distribution centers in supply chain network design. Computers & Industrial Engineering, 55(1), 64-79. https://doi.org/10.1016/j.cie.2007.12.001
Song, G. F., Yuan, Y. B., & Zhang, M. Y. (2008). Shopping mall location based on AHP and multi-level fuzzy comprehensive evaluation. Construction Management Modernization, 6, 13-16.
Torra, V. (2010). Hesitant fuzzy sets. International Journal of Intelligent Systems, 25(6), 529-539. https://doi.org/10.1002/int.20418
Wibowo, S., & Deng, H. (2013). Consensus-based decision support for multicriteria group decision making. Computers & Industrial Engineering, 66(4), 625-633. https://doi.org/10.1016/j.cie.2013.09.015
Wu, J., Dai, L. F., Chiclana, F., Fujita, H., & Herrera-Viedma, E. (2018). A minimum adjustment cost feedback mechanism based consensus model for group decision making under social network with distributed linguistic trust. Information Fusion, 41, 232-242. https://doi.org/10.1016/j.inffus.2017.09.012
Wu, Z. B., & Xu, J. P. (2018). A consensus model for large-scale group decision making with hesitant fuzzy information and changeable clusters. Information Fusion, 41, 217-231. https://doi.org/10.1016/j.inffus.2017.09.011
Xu, X. H., Zhong, X. Y., Chen, X. H., & Zhou, Y. J. (2015). A dynamical consensus method based on exit-delegation mechanism for large group emergency decision making. KnowledgeBased Systems, 86, 237-249. https://doi.org/10.1016/j.knosys.2015.06.006
Xu, Z. S. (2005). Deviation measures of linguistic preference relations in group decision making. Omega, 33(3), 249-254. https://doi.org/10.1016/j.omega.2004.04.008
Xu, Z. S. (2009). An automatic approach to reaching consensus in multiple attribute group decision making. Computers & Industrial Engineering, 56(4), 1369-1374. https://doi.org/10.1016/j.cie.2008.08.013
Zadeh, L. A. (1965). Fuzzy sets. Information & Control, 8(3), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
Ben-Arieh, D., & Chen, Z. F. (2006). Linguistic-labels aggregation and consensus measure for autocratic decision-making using group recommendations. IEEE Transactions on Systems, Man, and Cybernetics − Part A: Systems and Humans, 36(3), 558-568. https://doi.org/10.1109/TSMCA.2005.853488
Can, G. F., & Delice, E. K. (2018). A task-based fuzzy integrated MCDM approach for shopping mall selection considering universal design criteria. Soft Computing, 22(22), 7377-7397. https://doi.org/10.1007/s00500-018-3074-4
Canas, S. R. D., Ferreira, F. A. F., & Meidutė-Kavaliauskienė, I. (2015). Setting rents in residential real estate: a methodological proposal using multiple criteria decision analysis. International Journal of Strategic Property Management, 19(4), 368-380. https://doi.org/10.3846/1648715X.2015.1093562
Cheng, E. W. L., Li, H., & Yu, L. (2005). The analytic network process (ANP) approach to location selection: a shopping mall illustration. Construction Innovation, 5(2), 83-97. https://doi.org/10.1108/14714170510815195
Cheng, E. W. L., Li, H., & Yu, L. (2007). A GIS approach to shopping mall location selection. Building and Environment, 42(2), 884-892. https://doi.org/10.1016/j.buildenv.2005.10.010
Dong, Y. C., Zhang, G. Q., Hong, W. C., & Xu, Y. F. (2010). Consensus models for AHP group decision making under row geometric mean prioritization method. Decision Support Systems, 49(3), 281-289. https://doi.org/10.1016/j.dss.2010.03.003
Elevli, B. (2014). Logistics freight center locations decision by using Fuzzy-PROMETHEE. Transport, 29(4), 412-418. https://doi.org/10.3846/16484142.2014.983966
ElSamen, A. A. A., & Hiyasat R. I. (2017). Beyond the random location of shopping malls: a GIS perspective in Amman, Jordan. Journal of Retailing and Consumer Services, 34, 30-37. https://doi.org/10.1016/j.jretconser.2016.09.006
Gundogdu, C. E. (2013). Determination of the most suitable sites for shopping centers in geographical regions with GIS. Research in Logistics & Production, 3(2), 109-122.
Herrera, F., Herrera-Viedma, E., & Verdegay, J. L. (1996). Direct approach processes in group decision making using linguistic OWA operators. Fuzzy Sets and Systems, 79, 175-190. https://doi.org/10.1016/0165-0114(95)00162-X
Herrera-Viedma, E., Martínez, L., Mata, F., & Chiclana, F. (2005). A consensus support systems model for group decision making problems with multigranular linguistic preference relations. IEEE Transactions on Fuzzy Systems, 13(5), 644-658. https://doi.org/10.1109/TFUZZ.2005.856561
Kahraman, C., Engin, O., Kabak, O., & Kaya, I. (2009). Information systems outsourcing decisions using a GDM approach. Engineering Applications of Artificial Intelligence, 22(6), 832841. https://doi.org/10.1016/j.engappai.2008.10.009
Lee, H. S. (2002). Optimal consensus of fuzzy opinions under group decision making environment. Fuzzy Sets and Systems, 132(3), 303-315. https://doi.org/10.1016/S0165-0114(02)00056-8
Li, C. C., Dong, Y. C., Herrera, F., & Herrera-Viedma, E. (2017). Personalized individual semantics in computing with words for supporting linguistic group decision making. An application on consensus reaching. Information Fusion, 33, 29-40. https://doi.org/10.1016/j.inffus.2016.04.005
Liao, H. C., & Wu, X. L. (2019). DNMA: a double normalizationbased multiple aggregation method for multi-expert multicriteria decision making. Omega (in press). https://doi.org/10.1016/j.omega.2019.04.001
Liao, H. C., Qin, R., Gao, C. Y., Wu, X. L., Hafezalkotob, A., & Herrera, F. (2019). Score-HeDLiSF: a score function of hesitant fuzzy linguistic term set based on hesitant degrees and linguistic scale functions: an application to unbalanced hesitant fuzzy linguistic MULTIMOORA. Information Fusion, 48, 39-54. https://doi.org/10.1016/j.inffus.2018.08.006
Liao, H. C., Wu, X. L., Liang, X. D., Xu, J. P., & Herrera, F. (2018). A new hesitant fuzzy linguistic ORESTE method for hybrid multi-criteria decision making. IEEE Transactions on Fuzzy Systems, 26(6), 3793-3807. https://doi.org/10.1109/TFUZZ.2018.2849368
Liao, H. C., Wu, X. L., Mi, X. M., & Herrera, F. (2019). An integrated method for cognitive complex multiple experts multiple criteria decision making based on ELECTRE III with weighted Borda rule. Omega (in press). https://doi.org/10.1016/j.omega.2019.03.010
Liao, H. C., Xu, Z. S., & Zeng, X. J. (2015). Hesitant fuzzy linguistic VIKOR method and its application in qualitative multiple criteria decision making. IEEE Transactions on Fuzzy Systems, 23(5), 1343-1355. https://doi.org/10.1109/TFUZZ.2014.2360556
Liao, H. C., Xu, Z. S., Herrera-Viedma, E., & Herrera, F. (2018). Hesitant fuzzy linguistic term set and its application in decision making: a state-of-the-art survey. International Journal of Fuzzy Systems, 20(12), 1-27. https://doi.org/10.1007/s40815-017-0432-9
Liao, H. C., Xu, Z. S., Zeng, X. J., & Merigó, J. M. (2015). Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets. Knowledge-Based Systems, 76, 127-138. https://doi.org/10.1016/j.knosys.2014.12.009
Liu, Y., Liang, C., Chiclana, F., & Wu, J. (2017). A trust induced recommendation mechanism for reaching consensus in group decision making. Knowledge-Based Systems, 119, 221-231. https://doi.org/10.1016/j.knosys.2016.12.014
Parreiras, R. O., Ekel, P. Y., Martini, J. S. C., & Palhares, R. M. (2010). A flexible consensus scheme for multicriteria group decision making under linguistic assessments. Information Sciences, 180(7), 1075-1089. https://doi.org/10.1016/j.ins.2009.11.046
Perez, I. J., Cabrerizo, F. J., Alonso, S., & Herrera-Viedma, E. (2014). A new consensus model for group decision making problems with non-homogeneous experts. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 44(4), 494-498. https://doi.org/10.1109/TSMC.2013.2259155
Rodríguez, R. M., Martínez, L., & Herrera, F. (2012). Hesitant fuzzy linguistic term sets for decision making. IEEE Transactions on Fuzzy Systems, 20(1), 109-119. https://doi.org/10.1109/TFUZZ.2011.2170076
Ross, A., & Jayaraman, V. (2008). An evaluation of new heuristics for the location of cross-docks distribution centers in supply chain network design. Computers & Industrial Engineering, 55(1), 64-79. https://doi.org/10.1016/j.cie.2007.12.001
Song, G. F., Yuan, Y. B., & Zhang, M. Y. (2008). Shopping mall location based on AHP and multi-level fuzzy comprehensive evaluation. Construction Management Modernization, 6, 13-16.
Torra, V. (2010). Hesitant fuzzy sets. International Journal of Intelligent Systems, 25(6), 529-539. https://doi.org/10.1002/int.20418
Wibowo, S., & Deng, H. (2013). Consensus-based decision support for multicriteria group decision making. Computers & Industrial Engineering, 66(4), 625-633. https://doi.org/10.1016/j.cie.2013.09.015
Wu, J., Dai, L. F., Chiclana, F., Fujita, H., & Herrera-Viedma, E. (2018). A minimum adjustment cost feedback mechanism based consensus model for group decision making under social network with distributed linguistic trust. Information Fusion, 41, 232-242. https://doi.org/10.1016/j.inffus.2017.09.012
Wu, Z. B., & Xu, J. P. (2018). A consensus model for large-scale group decision making with hesitant fuzzy information and changeable clusters. Information Fusion, 41, 217-231. https://doi.org/10.1016/j.inffus.2017.09.011
Xu, X. H., Zhong, X. Y., Chen, X. H., & Zhou, Y. J. (2015). A dynamical consensus method based on exit-delegation mechanism for large group emergency decision making. KnowledgeBased Systems, 86, 237-249. https://doi.org/10.1016/j.knosys.2015.06.006
Xu, Z. S. (2005). Deviation measures of linguistic preference relations in group decision making. Omega, 33(3), 249-254. https://doi.org/10.1016/j.omega.2004.04.008
Xu, Z. S. (2009). An automatic approach to reaching consensus in multiple attribute group decision making. Computers & Industrial Engineering, 56(4), 1369-1374. https://doi.org/10.1016/j.cie.2008.08.013
Zadeh, L. A. (1965). Fuzzy sets. Information & Control, 8(3), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X