Abstract
The challenge of complex multi-attribute large group decision-making (CMALGDM) is reflected from three perspectives: interrelated attributes, large group decision makers (DMs) and dynamic decision environments. However, there are few decision techniques that can address the three perspectives simultaneously. This paper proposes a random intuitionistic fuzzy factor analysis model, aiming to address the challenge of CMALGDM from the three perspectives. The proposed method effectively reduces the dimensionality of the original data and takes into account the underlying random environmental factors which may affect the performances of alternatives. The development of this method follows three steps. First, the random intuitionistic fuzzy variables are developed to deal with a hybrid uncertain situation where fuzziness and randomness co-exist. Second, a novel factor analysis model for random intuitionistic fuzzy variables is proposed. This model uses specific mappings or functions to define the way in which evaluations are affected by the dynamic environment vector through data learning or prior distributions. Third, multiple correlated attribute variables and DM variables are transformed into fewer independent factors by a two-step procedure using the proposed model. In addition, the objective classifications and weights for attributes and DMs are obtained from the results of orthogonal rotated factor loading. An illustrative case and detailed comparisons of decision results in different environmental conditions are demonstrated to test the feasibility and validity of the proposed method.
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References
Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96.
Cazes, P., Chouakria, A., Diday, E., & Schektman, Y. (1997). Extension de l’analyse en composantes principales à des données de type intervalle. Revuede Statistique Appliquée, 45(3), 5–24.
Chen, D. P., Chu, X. N., Sun, X. W., Li, Y. P., & Su, Y. L. (2015). An Information Axiom based decision making approach under hybrid uncertain environments. Information Sciences, 312, 25–39.
Chen, X. H., Li, H., & Tan, C. Q. (2019). An intuitionstic fuzzy factorial analysis model for multi-attribute decision-making under random environment. Journal of the Operational Research Society, 70(1), 81–100.
Chen, X. H., & Liu, R. (2006). Improved clustering algorithm and its application in complex huge group decision-making. Systems Engineering and Electronics, 28(11), 1695–1699. (in Chinese).
Gou, X. J., & Xu, Z. S. (2017). Exponential operations for intuitionistic fuzzy numbers and interval numbers in multi-attribute decision making. Fuzzy Optimization and Decision Making, 16(2), 183–204.
Gou, X. J., Xu, Z. S., & Herrera, F. (2018). Consensus reaching process for large-scale group decision making with double hierarchy hesitant fuzzy linguistic preference relations. Knowledge-Based Systems, 157, 20–33.
Gupta, M., & Mohanty, B. K. (2016). An algorithmic approach to group decision making problems under fuzzy and dynamic environment. Expert Systems with Applications, 55, 118–132.
Labella, Á., Liu, Y., Rodríguez, R. M., & Martínez, L. (2018). Analyzing the performance of classical consensus models in large scale group decision making: A comparative study. Applied Soft Computing, 67, 677–690.
Lai, K. K., Wang, S. Y., Xu, J. P., Zhu, S. S., & Fang, Y. (2002). A class of linear interval programming problems and its application to portfolio selection. IEEE Transactions on Fuzzy Systems, 10(6), 698–704.
Li, J., & Xu, J. P. (2009). A novel portfolio selection model in a hybrid uncertain environment. Omega-International Journal of Management Science, 37(2), 439–449.
Liu, B. S., Shen, Y. H., Chen, X. H., Chen, Y., & Wang, X. Q. (2014a). A partial binary tree DEA-DA cyclic classification model for decision makers in complex multi-attribute large-group interval-valued intuitionistic fuzzy decision-making problems. Information Fusion, 18, 119–130.
Liu, B. S., Shen, Y. H., Chen, Y., Chen, X. H., & Wang, Y. M. (2015a). A two-layer weight determination method for complex multi-attribute large-group decision-making experts in a linguistic environment. Information Fusion, 23, 156–165.
Liu, B. S., Shen, Y. H., Chen, X. H., Sun, H., & Chen, Y. (2014b). A complex multi-attribute large-group PLS decision-making method in the interval-valued intuitionistic fuzzy environment. Applied Mathematical Modelling, 38(17–18), 4512–4527.
Liu, B. S., Shen, Y. H., Zhang, W., Chen, X. H., & Wang, X. Q. (2015b). An interval-valued intuitionistic fuzzy principal component analysis model-based method for complex multi-attribute large-group decision-making. European Journal of Operational Research, 245(1), 209–225.
Lourenzutti, R., & Krohling, R. A. (2016). A generalized TOPSIS method for group decision making with heterogeneous information in a dynamic environment. Information Sciences, 330, 1–18.
Lourenzutti, R., Krohling, R. A., & Reformat, M. Z. (2017). Choquet based TOPSIS and TODIM for dynamic and heterogeneous decision making with criteria interaction. Information Sciences, 408, 41–69.
Palomares, I., Martínez, L., & Herrera, F. (2014). A consensus model to detect and manage noncooperative behaviors in large-scale group decision making. IEEE Transactions on Fuzzy Systems, 22(3), 516–530.
Pei, Z. (2017). Multi-attribute decision making based on a novel IF point operator. Fuzzy Optimization and Decision Making, 16(4), 505–524.
Shi, Z. J., Wang, X. Q., Palomares, I., Guo, S. J., & Ding, R. X. (2018). A novel consensus model for multi-attribute large-scale group decision making based on comprehensive behavior classification and adaptive weight updating. Knowledge-Based Systems, 158, 196–208.
Spearman, C. (1904). General intelligence, objectively determined and measured. American Journal of Psychology, 15(2), 201–292.
Tan, C. Q., Jiang, Z. Z., Chen, X. H., et al. (2015). Atanassov’s intuitionistic fuzzy Quasi-Choquet geometric operators and their applications to multicriteria decision making. Fuzzy Optimization and Decision Making, 14(2), 139–172.
Xu, Z. S. (2007). Intuitionistic fuzzy aggregation operators. IEEE Transactions on Fuzzy Systems, 15(6), 1179–1187.
Xu, Z. S., & Yager, R. R. (2006). Some geometric aggregation operators based on intuitionistic fuzzy sets. International Journal of General Systems, 35(4), 417–433.
Zhang, X. M., & Xu, Z. S. (2012). A new method for ranking intuitionistic fuzzy values and its application in multi-attribute decision making. Fuzzy Optimization and Decision Making, 11(2), 135–146.
Acknowledgements
The authors gratefully acknowledge the financial support provided by the Major Project of National Nature Science Foundation of China (71790615), the National Nature Science Foundation of China (71671188, 71971218), the Key Project of National Nature Science Foundation of China (91846301), the Key Laboratory of Hunan Province for New Retail Virtual Reality Technology, Hunan University of Technology and Business (2017TP1026).
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Chen, X., Wu, M., Tan, C. et al. A random intuitionistic fuzzy factor analysis model for complex multi-attribute large group decision-making in dynamic environments. Fuzzy Optim Decis Making 20, 101–127 (2021). https://doi.org/10.1007/s10700-020-09334-9
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DOI: https://doi.org/10.1007/s10700-020-09334-9