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2016 | OriginalPaper | Buchkapitel

Dual Hesitant Fuzzy Soft Set and Its Properties

verfasst von : Hai-dong Zhang, Lan Shu

Erschienen in: Fuzzy Systems & Operations Research and Management

Verlag: Springer International Publishing

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Abstract

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. By combining the dual hesitant fuzzy set and soft set models, we introduce the concept of dual hesitant fuzzy soft sets. Further some operations on the dual hesitant fuzzy soft sets are investigated, such as complement operation, “AND” and “OR” operations, sum and product operations.

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Literatur
1.
Zurück zum Zitat Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986) Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)
2.
Zurück zum Zitat Babitha, K.V., John, S.J.: Hesitant fuzzy soft sets. J. New Results Sci. 3, 98–107 (2013) Babitha, K.V., John, S.J.: Hesitant fuzzy soft sets. J. New Results Sci. 3, 98–107 (2013)
3.
Zurück zum Zitat Chen, Y.F., Peng, X.D., Guan, G.H., Jiang, H.D.: Approaches to multiple attribute decision making based on the correlation coefficient with dual hesitant fuzzy information. J. Intell. Fuzzy Syst. 26, 2547–2556 (2014) Chen, Y.F., Peng, X.D., Guan, G.H., Jiang, H.D.: Approaches to multiple attribute decision making based on the correlation coefficient with dual hesitant fuzzy information. J. Intell. Fuzzy Syst. 26, 2547–2556 (2014)
4.
Zurück zum Zitat Deschrijver, G., Kerre, E.E.: Implicators based on binary aggregation operators in interval-valued fuzzy set theory. Fuzzy Sets Syst. 153, 229–248 (2005) Deschrijver, G., Kerre, E.E.: Implicators based on binary aggregation operators in interval-valued fuzzy set theory. Fuzzy Sets Syst. 153, 229–248 (2005)
5.
Zurück zum Zitat Farhadinia, B.: Correlation for dual hesitant fuzzy sets and dual interval-valued hesitant fuzzy sets. Int. J. Intell. Syst. 29, 184–205 (2014) Farhadinia, B.: Correlation for dual hesitant fuzzy sets and dual interval-valued hesitant fuzzy sets. Int. J. Intell. Syst. 29, 184–205 (2014)
6.
Zurück zum Zitat Gau, W.L., Buehrer, D.J.: Vague sets. IEEE Trans. Syst. Man Cybern. 23(2), 610–614 (1993) Gau, W.L., Buehrer, D.J.: Vague sets. IEEE Trans. Syst. Man Cybern. 23(2), 610–614 (1993)
7.
Zurück zum Zitat Jiang, Y., Tang, Y., Chen, Q., Liu, H., Tang, J.: Interval-valued intuitionistic fuzzy soft sets and their properties. Comput. Math. Appl. 60, 906–918 (2010) Jiang, Y., Tang, Y., Chen, Q., Liu, H., Tang, J.: Interval-valued intuitionistic fuzzy soft sets and their properties. Comput. Math. Appl. 60, 906–918 (2010)
8.
Zurück zum Zitat Molodtsov, D.: Soft set theory-First results. Comput. Math. Appl. 37, 19–31 (1999) Molodtsov, D.: Soft set theory-First results. Comput. Math. Appl. 37, 19–31 (1999)
9.
Zurück zum Zitat Maji, P.K., Biswas, R., Roy, A.R.: Fuzzy soft set. J. Fuzzy Math. 9(3), 589–602 (2001) Maji, P.K., Biswas, R., Roy, A.R.: Fuzzy soft set. J. Fuzzy Math. 9(3), 589–602 (2001)
10.
Zurück zum Zitat Maji, P.K.: More on intuitionistic fuzzy soft sets. Lect. Notes Comput. Sci 5908, 231–240 (2009) Maji, P.K.: More on intuitionistic fuzzy soft sets. Lect. Notes Comput. Sci 5908, 231–240 (2009)
11.
Zurück zum Zitat Maji, P.K., Biswas, R., Roy. A.R.: Intuitionistic fuzzy soft sets. J. Fuzzy Math. 9, 677–692 (2001) Maji, P.K., Biswas, R., Roy. A.R.: Intuitionistic fuzzy soft sets. J. Fuzzy Math. 9, 677–692 (2001)
12.
Zurück zum Zitat Maji, P.K., Biswas, R., Roy, A.R.: On intuitionistic fuzzy soft sets. J. Fuzzy Math. 12, 669–683 (2004) Maji, P.K., Biswas, R., Roy, A.R.: On intuitionistic fuzzy soft sets. J. Fuzzy Math. 12, 669–683 (2004)
13.
Zurück zum Zitat Miyamoto, S.: Multisets and fuzzy multisets. In: Liu, Z.Q., Miyamoto, S. (eds.) Soft Computing and Human-Centered Machines, pp. 9–33. Springer, Berlin, Germany (2000) Miyamoto, S.: Multisets and fuzzy multisets. In: Liu, Z.Q., Miyamoto, S. (eds.) Soft Computing and Human-Centered Machines, pp. 9–33. Springer, Berlin, Germany (2000)
14.
Zurück zum Zitat Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 145–172 (1982) Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 145–172 (1982)
15.
Zurück zum Zitat Torra, V., Narukawa, Y.: On hesitant fuzzy sets and decision. The 18th IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, pp. 1378–1382 (2009) Torra, V., Narukawa, Y.: On hesitant fuzzy sets and decision. The 18th IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, pp. 1378–1382 (2009)
16.
Zurück zum Zitat Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25, 529–539 (2010) Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25, 529–539 (2010)
17.
Zurück zum Zitat Wang, H.J., Zhao, X.F., Wei, G.W.: Dual hesitant fuzzy aggregation operators in multiple attribute decision making. J. Intell. Fuzzy Syst. 26, 2281–2290 (2014) Wang, H.J., Zhao, X.F., Wei, G.W.: Dual hesitant fuzzy aggregation operators in multiple attribute decision making. J. Intell. Fuzzy Syst. 26, 2281–2290 (2014)
18.
Zurück zum Zitat Xu, W., Ma, J., Wang, S.Y., Hao, G.: Vague soft sets and their properties. Comput. Math. Appl. 59, 787–794 (2010) Xu, W., Ma, J., Wang, S.Y., Hao, G.: Vague soft sets and their properties. Comput. Math. Appl. 59, 787–794 (2010)
19.
Zurück zum Zitat Ye, J.: Correlation coefficient of dual hesitant fuzzy sets and its application to multiple attribute decision making. Appl. Math. Modell. 38, 659–666 (2014) Ye, J.: Correlation coefficient of dual hesitant fuzzy sets and its application to multiple attribute decision making. Appl. Math. Modell. 38, 659–666 (2014)
20.
Zurück zum Zitat Yang, X.B., Lin, T.Y., Yang, J.Y., Li, Y., Yu, D.: Combination of interval-valued fuzzy set and soft set. Comput. Math. Appl. 58(3), 521–527 (2009) Yang, X.B., Lin, T.Y., Yang, J.Y., Li, Y., Yu, D.: Combination of interval-valued fuzzy set and soft set. Comput. Math. Appl. 58(3), 521–527 (2009)
21.
Zurück zum Zitat Yang, Y., Tan, X., Meng, C.C.: The multi-fuzzy soft set and its application in decision making. Appl. Math. Modell. 37, 4915–4923 (2013) Yang, Y., Tan, X., Meng, C.C.: The multi-fuzzy soft set and its application in decision making. Appl. Math. Modell. 37, 4915–4923 (2013)
22.
Zurück zum Zitat Zhu, B., Xu, Z.S., Xia, M.M.: Dual hesitant fuzzy sets. J. Appl. Math. 13, Article ID 879629 (2012) Zhu, B., Xu, Z.S., Xia, M.M.: Dual hesitant fuzzy sets. J. Appl. Math. 13, Article ID 879629 (2012)
23.
Zurück zum Zitat Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 378–352 (1965) Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 378–352 (1965)
Metadaten
Titel
Dual Hesitant Fuzzy Soft Set and Its Properties
verfasst von
Hai-dong Zhang
Lan Shu
Copyright-Jahr
2016
DOI
https://doi.org/10.1007/978-3-319-19105-8_17

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