Abstract
A novel hybrid soft set model called intertemporal hesitant fuzzy soft set is proposed, and then, it is showed how it can deal with group decision making problems. This model can be used to incorporate hesitant information that varies across time, when the alternatives are described by their degree of agreement with various characteristics. According to the period of time (whether it is indefinitely long or with a known termination date), the proposed model is, respectively, called long-term and short-term intertemporal hesitant fuzzy soft set. Corresponding group decision making approaches are provided, where the application of Quasi-Hyperbolic discounting permits to deal with the time-inconsistent experts’ preferences. Both the effect of scores of hesitant fuzzy elements and the effect of uncertainty contained in hesitant information are considered in the proposed decision approaches.
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References
Akram, M., Adeel, A., Alcantud, J.C.R.: Fuzzy \(N\)-soft sets: a novel model with applications. J. Intell. Fuzzy Syst. 35(11), 1–15 (2018)
Akram, M., Adeel, A., Alcantud, J.C.R.: Group decision-making methods based on hesitant \(N\)-soft sets. Expert Syst. Appl. 115, 95–105 (2019)
Alcantud, J.C.R.: A novel algorithm for fuzzy soft set based decision making from multiobserver input parameter data set. Inf. Fusion 29, 142–148 (2016)
Alcantud, J.C.R.: Some formal relationships among soft sets, fuzzy sets, and their extensions. Int. J. Approx. Reason. 68, 45–53 (2016)
Alcantud, J.C.R., Giarlotta, A.: Necessary and possible hesitant fuzzy sets: a novel model for group decision making. Inf. Fusion 46, 63–76 (2019)
Alcantud, J.C.R., Mathew, T.J.: Separable fuzzy soft sets and decision making with positive and negative attributes. Appl. Soft. Comput. 59, 586–595 (2017)
Alcantud, J.C.R., Santos-García, G.: A new criterion for soft set based decision making problems under incomplete information. Int. J. Comput. Intell. Syst. 10, 394–404 (2017)
Alcantud, J.C.R., Torra, V.: Decomposition theorems and extension principles for hesitant fuzzy sets. Inf. Fusion 41, 48–56 (2018)
Alcantud, J.C.R., Muñoz Torrecillas, M.A.J.: Intertemporal choice of fuzzy soft sets. Symmetry Basel 10(9), 371 (2018). https://doi.org/10.3390/sym10090371
Aliahmadipour, L., Torra, V., Eslami, E., Eftekhari, M.: A definition for hesitant fuzzy partitions. Int. J. Comput. Intell. Syst. 9(3), 497–505 (2016)
Berns, G.S., Laibson, D., Loewenstein, G.: Intertemporal choice-toward an integrative framework. Trends Cogn. Sci. 11(11), 482–488 (2007)
Bustince, H., Barrenechea, E., Pagola, M., Fernández, J., Xu, Z., Bedregal, B., Montero, J., Hagras, H., Herrera, F., Baets, B.D.: A historical account of types of fuzzy sets and their relationships. IEEE Trans. Fuzzy Syst. 24(1), 179–194 (2016)
Diamond, P., Köszegi, B.: Quasi-hyperbolic discounting and retirement. J. Public Econ. 87(9), 1839–1872 (2003)
Farhadinia, B.: Multicriteria decision making method based on the higher order hesitant fuzzy soft set. Int. Scholarly Res. Not. 2014, 1–11 (2014)
Farhadinia, B.: A series of score functions for hesitant fuzzy sets. Inf. Sci. 277(2), 102–110 (2014)
Fatimah, F., Rosadi, D., Hakim, R.B.F., Alcantud, J.C.R.: \(N\)-soft sets and their decision making algorithms. Soft Comput. 22(12), 3829–3842 (2018)
Feng, F., Jun, Y.B., Liu, X., Li, L.: An adjustable approach to fuzzy soft set based decision making. J. Comput. Appl. Math. 234(1), 10–20 (2010)
Fisher, I.: The Theory of Interest: As Determined by Impatience to Spend Income and Opportunity to Invest. Macmillan, New York (1930)
Kong, Z., Gao, L., Wang, L.: Comment on “A fuzzy soft set theoretic approach to decision making problems”. J. Comput. Appl. Math. 223(2), 540–542 (2009)
Krishankumar, R., Subrajaa, L.S., Ravichandran, K.S., Kar, S., Saeid, A.B.: A framework for multi-attribute group decision-making using double hierarchy hesitant fuzzy linguistic term set. Int. J. Fuzzy Syst. (2019). https://doi.org/10.1007/s40815-019-00618-w
Laibson, D.: Golden eggs and hyperbolic discounting. Quart. J. Econ. 112(2), 443–477 (1997)
Liu, Y., Luo, J., Wang, B., Qin, K.: A theoretical development on the entropy of interval-valued intuitionistic fuzzy soft sets based on the distance measure. Int. J. Comput. Intell. Syst. 10(1), 569–592 (2017)
Liu, Y., Qin, K., Martínez, L.: Improving decision making approaches based on fuzzy soft sets and rough soft sets. Appl. Soft. Comput. 65, 320–332 (2018)
Liu, Y., Qin, K., Rao, C., Mahamadu, M.A.: Object-parameter approaches to predicting unknown data in an incomplete fuzzy soft set. Int. J. Appl. Math. Comput. Sci. 27(1), 157–167 (2017)
Liu, Y., Zhao, H., Xu, Z.: An orthogonal clustering method under hesitant fuzzy environment. Int. J. Comput. Intell. Syst. 10(1), 663–676 (2017)
Loewenstein, G., Prelec, D.: Anomalies in intertemporal choice: evidence and an interpretation. Quart. J. Econ. 107(2), 573–597 (1992)
Molodtsov, D.: Soft set theory\(-\)first results. Comput. Math. Appl. 37(4–5), 19–31 (1999)
Phelps, E., Pollak, R.: On second-best national saving and game-equilibrium growth. The Rev. Econ. Stud. 35(2), 185–199 (1968)
Roy, A.R., Maji, P.: A fuzzy soft set theoretic approach to decision making problems. J. Comput. Appl. Math. 203(2), 412–418 (2007)
Samuelson, P.A.: A note on measurement of utility. Rev. Econ. Stud. 4(2), 155–161 (1937)
Shaheen, T., Mian, B., Shabir, M., Feng, F.: A novel approach to decision analysis using dominance-based soft rough sets. Int. J. Fuzzy Syst. 21(3), 954–962 (2019)
Streich, P., Levy, J.S.: Time horizons, discounting, and intertemporal choice. J. Confl. Resolut. 51(2), 199–226 (2007)
Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25(6), 529–539 (2010)
Wang, F., Li, X., Chen, X.: Hesitant fuzzy soft set and its applications in multicriteria decision making. J. Appl. Math. 7(3), 1–10 (2014)
Wang, H., Xu, Z.: Multi-groups decision making using intuitionistic-valued hesitant fuzzy information. Int. J. Comput. Intell. Syst. 9(3), 468–482 (2016)
Wang, L., Qin, K.: Robustness of general triple i method for fuzzy soft sets. Int. J. Comput. Intell. Syst. 11, 1111–1122 (2018)
Xu, Z., Xia, M.: Hesitant fuzzy entropy and cross-entropy and their use in multiattribute decision-making. In: IEEE global telecommunications conference on IEEE GLOBECOM 2007, pp. 700–704 (2007)
Xu, Z., Xia, M.: Hesitant fuzzy entropy and cross-entropy and their use in multiattribute decision-making. Int. J. Intell. Syst. 27(9), 799–822 (2012)
Yang, W., Pang, Y., Shi, J.: Linguistic hesitant intuitionistic fuzzy cross-entropy measures. Int. J. Comput. Intell. Syst. 10(1), 120–139 (2017)
Yu, W., Zhang, Z., Zhong, Q., Sun, L.: Extended TODIM for multi-criteria group decision making based on unbalanced hesitant fuzzy linguistic term sets. Comput. Ind. Eng. 114, 316–328 (2017)
Zhan, J., Ali, M.I., Mehmood, N.: On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods. Appl. Soft. Comput. 56, 446–457 (2017)
Zhan, J., Liu, Q., Herawan, T.: A novel soft rough set: soft rough hemirings and corresponding multicriteria group decision making. Appl. Soft. Comput. 54, 393–402 (2017)
Zhan, J., Zhu, K.: A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making. Soft Comput. 21(8), 1923–1936 (2017)
Zhang, Z., Guo, C., Martínez, L.: Managing multigranular linguistic distribution assessments in large-scale multiattribute group decision making. IEEE Trans. Syst. Man Cybern. -Syst. 47(11), 3063–3076 (2017)
Zhang, Z., Kou, X., Dong, Q.: Additive consistency analysis and improvement for hesitant fuzzy preference relations. Expert Syst. Appl. 98, 118–128 (2018)
Zhang, Z., Kou, X., Yu, W., Guo, C.: On priority weights and consistency for incomplete hesitant fuzzy preference relations. Knowledge Based Syst 143, 115–126 (2018)
Acknowledgements
This work is partially supported by the Spanish National Research Project TIN2015-66524-P and PGC2018-099402-B-I00, Spanish Ministry of Economy and Competitiveness, Postdoctoral fellow Ramón y Cajal (RYC-2017-21978), and the National Natural Science Foundation of China (Grant Nos. 61473239, 61603307).
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Liu, Y., Alcantud, J.C.R., Rodríguez, R.M. et al. Intertemporal Hesitant Fuzzy Soft Sets: Application to Group Decision Making. Int. J. Fuzzy Syst. 22, 619–635 (2020). https://doi.org/10.1007/s40815-020-00798-w
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DOI: https://doi.org/10.1007/s40815-020-00798-w