Abstract
Since the concept of fuzzy set was introduced, different extensions and generalizations have been proposed to manage the uncertainty in different problems. This chapter is focused in a recent extension so-called hesitant fuzzy set. Many researchers have paid attention on it and have proposed different extensions both in quantitative and qualitative contexts. Several concepts, basic operations and its extensions are revised in this chapter.
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References
Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)
Bedregal, B., Reiser, R., Bustince, H., López-Molina, C., Torra, V.: Aggregating functions for typical hesitant fuzzy elements and the action of automorphisms. Inf. Sci. 256(1), 82–97 (2014)
Beg, I., Rashid, T.: TOPSIS for hesitant fuzzy linguistic term sets. Int. J. Intell. Syst. 28, 1162–1171 (2013)
Chen, N., Xu, Z.S.: Properties of interval-valued hesitant fuzzy sets. J. Intell. Fuzzy Syst. 27(1), 143–158 (2014)
Chen, N., Xu, Z.S., Xia, M.M.: Interval-valued hesitant preference relations and their applications to group decision making. Knowl. Based Syst. 37(1), 528–540 (2013)
Chen, S.M., Hong, J.A.: Multicriteria linguistic decision making based on hesitant fuzzy linguistic term sets and the aggregation of fuzzy sets. Inf. Sci. 286, 63–74 (2014)
Chen, Y., Penga, X., Guanb, G., Jiangb, H.: Approaches to multiple attribute decision making based on the correlation coefficient with dual hesitant fuzzy information. J. Intell. Fuzzy Syst. 26(5), 2547–2556 (2014)
Chiclana, F., Herrera, F., Herrera-Viedma, E.: Integrating multiplicative preference relations in a multipurpose decision-making model based on fuzzy preference relations. Fuzzy Sets Syst. 122(2), 277–291 (2001)
Crawford, G., Williams, C.: A note on the analysis of subjective judgment matrices. J. Math. Psychol. 29(4), 387–405 (1985)
Dong, Y., Chen, X., Herrera, F.: Minimizing adjusted simple terms in the consensus reaching process with hesitant linguistic assessments in group decision making. Inf. Sci. 297, 95–117 (2015)
Dubois, D., Gottwald, S., Hajek, P., Kacprzyk, J., Prade, H.: Terminological difficulties in fuzzy set theory—the case of “intuitionistic fuzzy sets”. Fuzzy Sets Syst. 156(3), 485–491 (2005)
Farhadinia, B.: Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets. Inf. Sci. 240, 129–144 (2013)
Goguen, J.A.: L-fuzzy sets. J. Math. Anal. Appl. 18(1), 145–174 (1967)
Hesamian, G., Shams, M.: Measuring similarity and ordering based on hesitant fuzzy linguistic term sets. J. Intell. Fuzzy Syst. 28(2), 983–990 (2015)
Huang, H.C., Yang, X.: Pairwise comparison and distance measure of hesitant fuzzy linguistic term sets. Math. Probl. Eng. 1–8, 2014 (2014)
Ju, Y., Yang, S., Liu, X.: Some new dual hesitant fuzzy aggregation operators based on Choquet integral and their applications to multiple attribute decision making. J. Intell. Fuzzy Syst. 27(6), 2857–2868 (2014)
Ju, Y., Zhang, W., Yang, S.: Some dual hesitant fuzzy hamacher aggregation operators and their applications to multiple attribute decision making. J. Intell. Fuzzy Syst. 27(5), 2481–2495 (2014)
Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice-Hall PTR (1995)
Lee, L.W., Chen, S.M.: Fuzzy decision making based on likelihood-based comparison relations of hesitant fuzzy linguistic term sets and hesitant fuzzy linguistic operators. Inf. Sci. 294, 513–529 (2015)
Li, L.G., Peng, D.H.: Interval-valued hesitant fuzzy hamacher synergetic weighted aggregation operators and their application to shale gas areas selection. Math. Probl. Eng. 1–25, 2014 (2014)
Li, Y.B., Zhang, J.P.: Approach to multiple attribute decision making with hesitant triangular fuzzy information and their application to customer credit risk assessment. J. Intell. Fuzzy Syst. 26(6), 2853–2860 (2014)
Liao, H., Xu, Z.S., Zeng, X.J.: Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making. Inf. Sci. 271, 125–142 (2014)
Liao, H.C., Xu, Z.S.: A VIKOR-based method for hesitant fuzzy multi-criteria decision making. Fuzzy Optim. Decis. Making 12, 373–392 (2013)
Lin, R., Zhao, X., Wei, G.: Models for selecting an ERP system with hesitant fuzzy linguistic information. J. Intell. Fuzzy Syst. 26(5), 2155–2165 (2014)
Liu, H., Rodríguez, R.M.: A fuzzy envelope for hesitant fuzzy linguistic term set and its application to multicriteria decision making. Inf. Sci. 258, 266–276 (2014)
Martínez, L., Liu, J., Yang, J.B., Herrera, F.: A multigranular hierarchical linguistic model for design evaluation based on safety and cost analysis. Int. J. Intell. Syst. 20(12), 1161–1194 (2005)
Mendel, J.M., John, R.I.: Type-2 fuzzy sets made simple. IEEE Trans. Fuzzy Syst. 10(2), 117–127 (2002)
Meng, F., Chen, X.: An approach to interval-valued hesitant fuzzy multi-attribute decision making with incomplete weight information based on hybrid Shapley operators. Informatica 25(4), 617–642 (2014)
Pei, Z., Yi, L.: A note on operations of hesitant fuzzy sets. Int. J. Comput. Intell. Syst. 8(2), 226–239 (2015)
Peng, D.H., Wang, T.D., Gao, C.Y., Wang, H.: Continuous hesitant fuzzy aggregation operators and their application to decision making under interval-valued hesitant fuzzy setting. Sci. World J. 1–20, 2014 (2014)
Qian, G., Wang, H., Feng, X.: Generalized hesitant fuzzy sets and their application in decision support system. Knowl. Based Syst. 37(1), 357–365 (2013)
Rodríguez, R.M., Martínez, L., Herrera, F.: Hesitant fuzzy linguistic term sets for decision making. IEEE Trans. Fuzzy Syst. 20(1), 109–119 (2012)
Rodríguez, R.M., Martínez, L., Herrera, F.: A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets. Inf. Sci. 241(1), 28–42 (2013)
Rodríguez, R.M., Martínez, L., Torra, V., Xu, Z.S., Herrera, F.: Hesitant fuzzy sets: state of the art and future directions. Int. J. Intell. Syst. 29(6), 495–524 (2014)
Saaty, L.T.: The Analytic Hierarchy Process. McGraw-Hill (1980)
Saaty, R.W.: The analytic hierarchy process-what it is and how it is used. Math. Model. 9(3–5), 161–176 (1987)
Sahu, S.K., Sahu, N., Thakur, R.S., Thakur, G.S.: Hesitant fuzzy linguistic term set based document classification. In: Proceedings of the International Conference on Communication Systems and Network Technologies, pp. 586–590, Gwalior, India (2013)
Shi, J., Meng, C., Liu, Y.: Approach to multiple attribute decision making based on the intelligence computing with hesitant triangular fuzzy information and their application. J. Intell. Fuzzy Syst. 27(2), 701–707 (2014)
Singh, P.: A new method for solving dual hesitant fuzzy assignment problems with restrictions based on similarity measure. Appl. Soft Comput. 24, 559–571 (2014)
Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25(6), 529–539 (2010)
Torra, V.: Artificial intelligence research and development, chapter on the derivation of weights using the geometric mean approach for set-valued matrices. In: Frontiers in Artificial Intelligence and Applications, pp. 193–201 (2014)
Torra, V.: Derivation of priorities and weights for set-valued matrices using the geometric mean approach. Appl. Artif. Intell. 29(5), 500–513 (2015)
Torra, V., Narukawa, Y.: Modeling decisions: information fusion and aggregation operators. Springer, Heidelberg (2007)
Torra, V., Narukawa, Y.: On hesitant fuzzy sets and decision. In: Proceedings of the 18th IEEE International Conference on Fuzzy Systems, pp. 1378–1382 (2009)
Türksen, I.B.: Interval valued fuzzy sets based on normal forms. Fuzzy Sets Syst. 20, 191–210 (1986)
Wang, C., Li, Q., Zhou, X.: Multiple attribute decision making based on generalized aggregation operators under dual hesitant fuzzy environment. J. Appl. Math. 1–12, 2014 (2014)
Wang, C., Li, Q., Zhou, X., Yang, T.: Hesitant triangular fuzzy information aggregation operators based on bonferroni means and their application to multiple attribute decision making. Sci. World J. 1–15, 2014 (2014)
Wang, H.: Extended hesitant fuzzy linguistic term sets and their aggregation in group decision making. Int. J. Comput. Intell. Syst. 8(1), 14–33 (2015)
Wang, H., Xu, Z.S.: Some consistency measures of extended hesitant fuzzy linguistic preference relations. Inf. Sci. 297, 316–331 (2015)
Wang, H., Zhao, X., Wei, G.: Dual hesitant fuzzy aggregation operators in multiple attribute decision making. J. Intell. Fuzzy Syst. 26(5), 2281–2290 (2014)
Wang, J.Q., Wang, J., Chen, Q.H., Zhang, H.Y., Chen, X.H.: An outranking approach for multi-criteria decision-making with hesitant fuzzy linguistic term sets. Inf. Sci. 280, 338–351 (2014)
Wang, J.Q., Wu, J.T., Wang, J., Zhang, H.Y., Chen, X.H.: Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems. Inf. Sci. 288, 55–72 (2014)
Wang, L., Ni, M., Zhu, L.: Correlation measures of dual hesitant fuzzy sets. J. Appl. Math. 1–12, 2013 (2013)
Wei, C., Ren, Z., Rodríguez, R.M.: A hesitant fuzzy linguistic TODIM method based on a score function. Int. J. Comput. Intell. Syst. 8(4), 701–712 (2015)
Wei, C., Zhao, N., Tang, X.: Operators and comparisons of hesitant fuzzy linguistic term sets. IEEE Trans. Fuzzy Syst. 22(3), 575–585 (2014)
Wei, G., Lin, R., Wang, H.: Distance and similarity measures for hesitant interval-valued fuzzy sets. J. Intell. Fuzzy Syst. 27(1), 19–36 (2014)
Wei, G., Wang, H., Zhao, X., Lin, R.: Hesitant triangular fuzzy information aggregation in multiple attribute decision making. J. Intell. Fuzzy Syst. 26(3), 1201–1209 (2014)
Wei, G., Zhao, X.: Induced hesitant interval-valued fuzzy Einstein aggregation operators and their application to multiple attribute decision making. J. Intell. Fuzzy Syst. 24(4), 789–803 (2013)
Wei, G., Zhao, X., Lin, R.: Some hesitant interval-valued fuzzy aggregation operators and their applications to multiple attribute decision making. Knowl. Based Syst. 46, 43–53 (2013)
Wei, G., Zhao, X., Lin, R.: Models for hesitant interval-valued fuzzy multiple attribute decision making based on the correlation coefficient with incomplete weight information. J. Intell. Fuzzy Syst. 26(4), 1631–1644 (2014)
Xia, M.M., Xu, Z.S.: Hesitant fuzzy information aggregation in decision making. Int. J. Approx. Reason. 52, 395–407 (2011)
Xia, M.M., Xu, Z.S.: Managing hesitant information in GDM problems underfuzzy and multiplicative preference relations. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 21(06), 865–897 (2013)
Yang, S., Ju, Y.: Dual hesitant fuzzy linguistic aggregation operators and their applications to multi-attribute decision making. J. Intell. Fuzzy Syst. 27(4), 1935–1947 (2014)
Yavuz, M., Oztaysi, B., Cevik Onar, S., Kahraman, C.: Multi-criteria evaluation of alternative-fuel vehicles via a hierarchical hesitant fuzzy linguistic model. Expert Syst. Appl. 42(5), 2835–2848 (2015)
Ye, J.: Correlation coefficient of dual hesitant fuzzy sets and its application to multiple attribute decision making. Appl. Math. Model. 38(2), 659–666 (2014)
Yu, D.: Triangular hesitant fuzzy set and its application to teaching quality evaluation. J. Inf. Comput. Sci. 10(7), 1925–1934 (2013)
Yu, D.: Some generalized dual hesitant fuzzy geometric aggregation operators and applications. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 22(3), 367–384 (2014)
Yu, D., Li, D.F.: Dual hesitant fuzzy multi-criteria decision making and its application to teaching quality assessment. J. Intell. Fuzzy Syst. 27(4), 1679–1688 (2014)
Zadeh, L.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Zhang, Y.: Research on the computer network security evaluation based on the DHFHCG operator with dual hesitant fuzzy information. J. Intell. Fuzzy Syst. 28(1), 199–204 (2015)
Zhang, Z., Wu, C.: A decision support model for group decision making with hesitant multiplicative preference relations. Inf. Sci. 282, 136–166 (2014)
Zhang, Z., Wu, C.: Hesitant fuzzy linguistic aggregation operators and their applications to multiple attribute group decision making. J. Intell. Fuzzy Syst. 26(5), 2185–2202 (2014)
Zhang, Z., Wu, C.: On the use of multiplicative consistency in hesitant fuzzy linguistic preference relations. Knowl. Based Syst. 72, 13–27 (2014)
Zhao, X., Lin, R., Wei, G.: Hesitant triangular fuzzy information aggregation based on Einstein operations and their application to multiple attribute decision making. Expert Syst. Appl. 41(4, Part 1), 1086–1094
Zhong, G., Xu, L.: Models for multiple attribute decision making method in hesitant triangular fuzzy setting. J. Intell. Fuzzy Syst. 26(5), 2167–2174 (2014)
Zhu, B., Xu, Z.S.: Regression methods for hesitant fuzzy preference relations. Technol. Econ. Dev. Econ. 19, S214–S227 (2013)
Zhu, B., Xu, Z.S.: Consistency measures for hesitant fuzzy linguistic preference relations. IEEE Trans. Fuzzy Syst. 22, 35–45 (2014)
Zhu, B., Xu, Z.S.: Stochastic preference analysis in numerical preference relations. Eur. J. Oper. Res. 237(2), 628–633 (2014)
Zhu, B., Xu, Z.S., Xia, M.M.: Dual hesitant fuzzy sets. J. Appl. Math. 1–13, 2012 (2012)
Zhu, J.Q., Fu, F., Yin, K.X., Luo, J.Q., Wei, D.: Approaches to multiple attribute decision making with hesitant interval-valued fuzzy information under correlative environment. J. Intell. Fuzzy Syst. 27(2), 1057–1065 (2014)
Acknowledgements
This work is partially funded by the Spanish research projects TIN2011-27076-C03-03, TIN2015-66524-P, the Spanish Ministry of Economy and Finance Postdoctoral Training (FPDI-2013-18193) and ERDF.
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Rodríguez, R.M., Martínez, L., Herrera, F., Torra, V. (2016). A Review of Hesitant Fuzzy Sets: Quantitative and Qualitative Extensions. In: Kahraman, C., Kaymak, U., Yazici, A. (eds) Fuzzy Logic in Its 50th Year. Studies in Fuzziness and Soft Computing, vol 341. Springer, Cham. https://doi.org/10.1007/978-3-319-31093-0_5
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