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Erschienen in: Cognitive Computation 1/2017

16.12.2016

Distance and Aggregation-Based Methodologies for Hesitant Fuzzy Decision Making

verfasst von: B. Farhadinia, Zeshui Xu

Erschienen in: Cognitive Computation | Ausgabe 1/2017

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Abstract

Hesitant fuzzy set (HFS) as an effective tool to reflect human’s hesitancy has received great attention in recent years. The importance weights of possible values in hesitant fuzzy elements (HFEs), which are the basic units of a HFS, have not been taken into account in the existing literature. Thus, the frequently used HFEs cannot deal with the situations where all the possible values are provided by experts with different levels of expertise. Consequently, in this paper, we propose an extension of typical HFS called the ordered weighted hesitant fuzzy set (OWHFS). The basic units of an OWHFS allow the membership of a given element to be defined in terms of several possible values together with their importance weights. Moreover, in order to indicate that the OWHFS has a good performance in decision making, we first present some information measures and several aggregation operators for OWHFSs. Then, we apply them to multi-attribute decision making with ordered weighted hesitant fuzzy information.

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Literatur
1.
Zurück zum Zitat Akusok A, Miche Y, Hegedus J, Nian R, Lendasse A. A two stage methodology using K-NN and false-positive minimizing ELM for nominal data classification. Cogn Comput 2014;6:432–445.CrossRef Akusok A, Miche Y, Hegedus J, Nian R, Lendasse A. A two stage methodology using K-NN and false-positive minimizing ELM for nominal data classification. Cogn Comput 2014;6:432–445.CrossRef
2.
Zurück zum Zitat Atanassov K. Intuitionistic Fuzzy Sets: Theory and Applications, Physica-Verlag. Heidelberg: NewYork; 1999.CrossRef Atanassov K. Intuitionistic Fuzzy Sets: Theory and Applications, Physica-Verlag. Heidelberg: NewYork; 1999.CrossRef
3.
Zurück zum Zitat Atanassov K. Intuitionistic fuzzy sets. Fuzzy Sets Syst 1986;20:87–96.CrossRef Atanassov K. Intuitionistic fuzzy sets. Fuzzy Sets Syst 1986;20:87–96.CrossRef
4.
Zurück zum Zitat Atanassov K, Gargov G. Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 1989;31:343–349.CrossRef Atanassov K, Gargov G. Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 1989;31:343–349.CrossRef
5.
Zurück zum Zitat Bustince H. Indicator of inclusion grade for interval-valued fuzzy sets: application to approximate reasoning based on interval-valued fuzzy sets. Int J Approx Reason 2000;23(3):137–209.CrossRef Bustince H. Indicator of inclusion grade for interval-valued fuzzy sets: application to approximate reasoning based on interval-valued fuzzy sets. Int J Approx Reason 2000;23(3):137–209.CrossRef
6.
Zurück zum Zitat Bustince H, Burillo P. Vague sets are intuitionistic fuzzy sets. Fuzzy Sets Syst 1996;79:403–405.CrossRef Bustince H, Burillo P. Vague sets are intuitionistic fuzzy sets. Fuzzy Sets Syst 1996;79:403–405.CrossRef
7.
Zurück zum Zitat Czubenko M, Kowalczuk Z, Ordys A. Autonomous driver based on an intelligent system of decision-making. Cogn Comput 2015;7:569–581.CrossRef Czubenko M, Kowalczuk Z, Ordys A. Autonomous driver based on an intelligent system of decision-making. Cogn Comput 2015;7:569–581.CrossRef
8.
Zurück zum Zitat Dubois D, Prade H. Fuzzy Sets and Systems Theory and Applications. New York: Kluwer Academic; 1980. Dubois D, Prade H. Fuzzy Sets and Systems Theory and Applications. New York: Kluwer Academic; 1980.
9.
Zurück zum Zitat Farhadinia B. A novel method of ranking hesitant fuzzy values for multiple attribute decision-making problems. Int J Intell Syst 2013;28:752–767.CrossRef Farhadinia B. A novel method of ranking hesitant fuzzy values for multiple attribute decision-making problems. Int J Intell Syst 2013;28:752–767.CrossRef
10.
Zurück zum Zitat Farhadinia B. Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets. Inf Sci 2013; 240:129–144.CrossRef Farhadinia B. Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets. Inf Sci 2013; 240:129–144.CrossRef
11.
Zurück zum Zitat Farhadinia B. Distance and similarity measures for higher order hesitant fuzzy sets. Knowl-Based Syst 2014; 55:43–48.CrossRef Farhadinia B. Distance and similarity measures for higher order hesitant fuzzy sets. Knowl-Based Syst 2014; 55:43–48.CrossRef
12.
Zurück zum Zitat Farhadinia B. Correlation for dual hesitant fuzzy sets and dual interval-valued hesitant fuzzy sets. Int J Intell Syst 2014;29:184–205.CrossRef Farhadinia B. Correlation for dual hesitant fuzzy sets and dual interval-valued hesitant fuzzy sets. Int J Intell Syst 2014;29:184–205.CrossRef
13.
Zurück zum Zitat Farhadinia B. A series of score functions for hesitant fuzzy sets. Inf Sci 2014;277:102–110.CrossRef Farhadinia B. A series of score functions for hesitant fuzzy sets. Inf Sci 2014;277:102–110.CrossRef
14.
Zurück zum Zitat Farhadinia B. Multi criteria decision making method based on the higher order hesitant fuzzy soft set. Int Scholar Research Notices 2014. Hindawi. Farhadinia B. Multi criteria decision making method based on the higher order hesitant fuzzy soft set. Int Scholar Research Notices 2014. Hindawi.
15.
Zurück zum Zitat Farhadinia B. Hesitant fuzzy set lexicographical ordering and its application to multi-attribute decision making. Inf Sci 2016;327:233–245.CrossRef Farhadinia B. Hesitant fuzzy set lexicographical ordering and its application to multi-attribute decision making. Inf Sci 2016;327:233–245.CrossRef
16.
Zurück zum Zitat Farhadinia B. Multiple criteria decision making methods with completely unknown weights in hesitant fuzzy linguistic term setting. Knowl-Based Syst 2016;93:135–144.CrossRef Farhadinia B. Multiple criteria decision making methods with completely unknown weights in hesitant fuzzy linguistic term setting. Knowl-Based Syst 2016;93:135–144.CrossRef
17.
Zurück zum Zitat Rodriguez RM, Bedregal B, Bustince H, Dong YC, Farhadinia B, Kahraman C, Martinez L, Torra V, Xu YJ, Xu ZS, Herrera F. A position and perspective analysis of hesitant fuzzy sets on information fusion in decision making. Towards high quality progress. Inf Fusion 2016;29:89–97.CrossRef Rodriguez RM, Bedregal B, Bustince H, Dong YC, Farhadinia B, Kahraman C, Martinez L, Torra V, Xu YJ, Xu ZS, Herrera F. A position and perspective analysis of hesitant fuzzy sets on information fusion in decision making. Towards high quality progress. Inf Fusion 2016;29:89–97.CrossRef
18.
19.
Zurück zum Zitat Gorzalczany MB. A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 1987;21:1–17.CrossRef Gorzalczany MB. A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 1987;21:1–17.CrossRef
20.
Zurück zum Zitat Kahraman C, Kaya I. A fuzzy multicriteria methodology for selection among energy alternatives. Expert Syst Appl 2010;37:6270–6281.CrossRef Kahraman C, Kaya I. A fuzzy multicriteria methodology for selection among energy alternatives. Expert Syst Appl 2010;37:6270–6281.CrossRef
21.
Zurück zum Zitat Klir GJ, Yuan B. Fuzzy Sets and Fuzzy Logic: Theory and Applications. Upper Saddle River: Prentice-Hall; 1995. Klir GJ, Yuan B. Fuzzy Sets and Fuzzy Logic: Theory and Applications. Upper Saddle River: Prentice-Hall; 1995.
22.
Zurück zum Zitat Meng FY, Chen XH. Correlation coefficients of hesitant fuzzy sets and their application based on fuzzy measures. Cogn Comput 2015;7:445–463.CrossRef Meng FY, Chen XH. Correlation coefficients of hesitant fuzzy sets and their application based on fuzzy measures. Cogn Comput 2015;7:445–463.CrossRef
23.
Zurück zum Zitat Meng FY, Wang C, Chen XH. Linguistic interval hesitant fuzzy sets and their application in decision making. Cogn Comput 2016;8:52–68.CrossRef Meng FY, Wang C, Chen XH. Linguistic interval hesitant fuzzy sets and their application in decision making. Cogn Comput 2016;8:52–68.CrossRef
24.
Zurück zum Zitat Mitchell HB. Pattern recognition using type-II fuzzy sets. Inf Sci 2005;2-4:409–418.CrossRef Mitchell HB. Pattern recognition using type-II fuzzy sets. Inf Sci 2005;2-4:409–418.CrossRef
25.
Zurück zum Zitat Miyamoto S. Fuzzy multisets and their generalizations. Multiset Processing 2001;2235:225–235.CrossRef Miyamoto S. Fuzzy multisets and their generalizations. Multiset Processing 2001;2235:225–235.CrossRef
26.
Zurück zum Zitat Mizumoto M, Tanaka K. Some properties of fuzzy sets of type-2. Inf Control 1976;31:312–340.CrossRef Mizumoto M, Tanaka K. Some properties of fuzzy sets of type-2. Inf Control 1976;31:312–340.CrossRef
27.
Zurück zum Zitat Torra V. Hesitant fuzzy sets. Int J Intell Syst 2010;25:529– 539. Torra V. Hesitant fuzzy sets. Int J Intell Syst 2010;25:529– 539.
28.
Zurück zum Zitat Peng DH, Gao CY, Gao ZF. Generalized hesitant fuzzy synergetic weighted distance measures and their application to multiple criteria decision making. Appl Math Model 2013;37:5837– 5850.CrossRef Peng DH, Gao CY, Gao ZF. Generalized hesitant fuzzy synergetic weighted distance measures and their application to multiple criteria decision making. Appl Math Model 2013;37:5837– 5850.CrossRef
29.
Zurück zum Zitat Rodriguez RM, Martinez L, Herrera F. Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Syst 2012;20:109–119. Rodriguez RM, Martinez L, Herrera F. Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Syst 2012;20:109–119.
30.
Zurück zum Zitat Turksen IB. Interval valued fuzzy sets based on normal forms. Fuzzy Sets Syst 1986;20:191–210.CrossRef Turksen IB. Interval valued fuzzy sets based on normal forms. Fuzzy Sets Syst 1986;20:191–210.CrossRef
31.
Zurück zum Zitat Wei GW. Hesitant fuzzy prioritized operators and their application to multiple attribute decision making. Knowl-Based Syst 2012;31:176–182.CrossRef Wei GW. Hesitant fuzzy prioritized operators and their application to multiple attribute decision making. Knowl-Based Syst 2012;31:176–182.CrossRef
32.
Zurück zum Zitat Wei GW, Lan G. Grey relational analysis method for interval-valued intuitionistic fuzzy multiple attribute decision making. 5th International Conference on Fuzzy Systems and Knowledge Discovery; 2008. p. 291–295. Wei GW, Lan G. Grey relational analysis method for interval-valued intuitionistic fuzzy multiple attribute decision making. 5th International Conference on Fuzzy Systems and Knowledge Discovery; 2008. p. 291–295.
33.
Zurück zum Zitat Wei GW, Zhao XF, Lin v. Some hesitant interval-valued aggregation operators and their applications to multiple attribute decision making. Knowl-Based Syst 2013;46:43–53.CrossRef Wei GW, Zhao XF, Lin v. Some hesitant interval-valued aggregation operators and their applications to multiple attribute decision making. Knowl-Based Syst 2013;46:43–53.CrossRef
34.
Zurück zum Zitat Wu D, Mendel JM. A vector similarity measure for linguistic approximation: interval type-2 and type-1 fuzzy sets. Inf Sci 2008;178(2):381–402.CrossRef Wu D, Mendel JM. A vector similarity measure for linguistic approximation: interval type-2 and type-1 fuzzy sets. Inf Sci 2008;178(2):381–402.CrossRef
35.
Zurück zum Zitat Xia MM, Xu ZS. Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 2011; 52:395–407.CrossRef Xia MM, Xu ZS. Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 2011; 52:395–407.CrossRef
36.
Zurück zum Zitat Xu ZS. Deviation measures of linguistic preference relations in group decision making. Omega 2005;17:432–445. Xu ZS. Deviation measures of linguistic preference relations in group decision making. Omega 2005;17:432–445.
37.
Zurück zum Zitat Xu ZS, Xia MM. Distance and similarity measures for hesitant fuzzy sets. Inf Sci 2011;181:2128–2138.CrossRef Xu ZS, Xia MM. Distance and similarity measures for hesitant fuzzy sets. Inf Sci 2011;181:2128–2138.CrossRef
38.
Zurück zum Zitat Yager RR. On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans Syst Man Cybern 1988;18:183–190.CrossRef Yager RR. On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans Syst Man Cybern 1988;18:183–190.CrossRef
39.
Zurück zum Zitat Yang J, Gong LY, Tang YF, Yan J, He HB, Zhang LQ, Li G. An improved SVM-based cognitive diagnosis algorithm for operation states of distribution grid. Cogn Comput 2015;7:582–593.CrossRef Yang J, Gong LY, Tang YF, Yan J, He HB, Zhang LQ, Li G. An improved SVM-based cognitive diagnosis algorithm for operation states of distribution grid. Cogn Comput 2015;7:582–593.CrossRef
40.
Zurück zum Zitat Yu DJ. Some hesitant fuzzy information aggregation operators based on Einstein operational laws. Int J Intell Syst 2014;00:1– 21. Yu DJ. Some hesitant fuzzy information aggregation operators based on Einstein operational laws. Int J Intell Syst 2014;00:1– 21.
41.
Zurück zum Zitat Zadeh LA. Fuzzy sets. Inf Comput 1965;8:338–353. Zadeh LA. Fuzzy sets. Inf Comput 1965;8:338–353.
42.
Zurück zum Zitat Zhang Z, Wu C. Weighted hesitant fuzzy sets and their application to multi-criteria decision making. British J Math Comput Sci 2014;4:1091–1123.CrossRef Zhang Z, Wu C. Weighted hesitant fuzzy sets and their application to multi-criteria decision making. British J Math Comput Sci 2014;4:1091–1123.CrossRef
43.
Zurück zum Zitat Tian ZP, Wang J, Wang JQ, Zhang HY. A likelihood-based qualitative flexible approach with hesitant fuzzy linguistic information. Cogn Comput 2016. doi:10.1007/s12559-016-9400-1. Tian ZP, Wang J, Wang JQ, Zhang HY. A likelihood-based qualitative flexible approach with hesitant fuzzy linguistic information. Cogn Comput 2016. doi:10.​1007/​s12559-016-9400-1.
44.
Zurück zum Zitat Zhu B, Xu ZS. Hesitant fuzzy Bonferroni means for multi-criteria decision making. J Oper Res Soc 2013; 64:1831–1840.CrossRef Zhu B, Xu ZS. Hesitant fuzzy Bonferroni means for multi-criteria decision making. J Oper Res Soc 2013; 64:1831–1840.CrossRef
45.
Zurück zum Zitat Zhu B, Xu ZS, Xia MM. Dual hesitant fuzzy sets. J Appl Math 2012;2012:1–13. Zhu B, Xu ZS, Xia MM. Dual hesitant fuzzy sets. J Appl Math 2012;2012:1–13.
46.
Zurück zum Zitat Zhu B, Xu ZS, Xia MM. Hesitant fuzzy geometric Bonferroni means. Inf Sci 2012:72–85. Zhu B, Xu ZS, Xia MM. Hesitant fuzzy geometric Bonferroni means. Inf Sci 2012:72–85.
Metadaten
Titel
Distance and Aggregation-Based Methodologies for Hesitant Fuzzy Decision Making
verfasst von
B. Farhadinia
Zeshui Xu
Publikationsdatum
16.12.2016
Verlag
Springer US
Erschienen in
Cognitive Computation / Ausgabe 1/2017
Print ISSN: 1866-9956
Elektronische ISSN: 1866-9964
DOI
https://doi.org/10.1007/s12559-016-9436-2

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