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Hesitant Fuzzy Set and Its Extensions

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Hesitant Fuzzy Decision Making Methodologies and Applications

Part of the book series: Uncertainty and Operations Research ((UOR))

Abstract

As uncertainty takes place almost everywhere in our daily life, many different tools have been developed to recognize, represent, manipulate, and tackle such uncertainty.

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References

  • Atanassov KT (1983) lntuitionistic fuzzy sets. In: VII ITKR's Session, Sgurev V (Ed.), Sofia.

    Google Scholar 

  • Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96

    Article  Google Scholar 

  • Atanassov KT (2009) Remark on operations “subtraction” over intuitionistic fuzzy sets. Notes Intuitionistic Fuzzy Sets 15(3):20–24

    Google Scholar 

  • Atanassov KT (2012) On intuitionistic fuzzy sets theory. Springer, Berlin

    Book  Google Scholar 

  • Atanassov KT, Gargov G (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31:343–349

    Article  Google Scholar 

  • Atanassov KT, Riečan B (2006) On two operations over intuitionistic fuzzy sets. J Appl Math Stat Inform 2(2):145–148

    Google Scholar 

  • Behzadian M, Kazemzadeh RB, Albadvi A, Aghdasi M (2010) PROMETHEE: a comprehensive literature review on methodologies and applications. Eur J Oper Res 200:198–215

    Article  Google Scholar 

  • Bezdek JC (1993) Fuzzy models-what are they, and why? IEEE Trans Fuzzy Syst 1(1):1–6

    Article  Google Scholar 

  • Chen TY (2007) Remarks on the subtraction and division operations over intuitionistic fuzzy sets and interval-valued fuzzy sets. J Intell Fuzzy Syst 9(3):169–172

    Google Scholar 

  • Chen N, Xu ZS (2014) Properties of interval-valued hesitant fuzzy sets. J Intell Fuzzy Syst 27(1):143–158

    Google Scholar 

  • Chen N, Xu ZS, Xia MM (2013) Interval-valued hesitant preference relations and their applications to group decision making. Knowl-Based Syst 37:528–540

    Article  Google Scholar 

  • Chen N, Xu ZS, Xia MM (2015) The ELECTRE I multi-criteria decision making method based on hesitant fuzzy sets. Int J Inf Technol Decis Making 14(3):621–657

    Article  Google Scholar 

  • Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic Press, London

    Google Scholar 

  • Herrera F, Herrera-Viedma E (2000) Linguistic decision analysis: steps for solving decision problems under linguistic information. Fuzzy Sets Syst 115:67–82

    Article  Google Scholar 

  • Herrera F, Martínez L (2000) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8:746–752

    Article  Google Scholar 

  • Hong DH, Choi CH (2000) Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst 114:103–113

    Article  Google Scholar 

  • Liao HC, Xu ZS (2013) A VIKOR-based method for hesitant fuzzy multi-criteria decision making. Fuzzy Optim Decis Making 12(4):373–392

    Article  Google Scholar 

  • Liao HC, Xu ZS (2014a) Subtraction and division operations over hesitant fuzzy sets. J Intell Fuzzy Syst 27(1):65–72

    Google Scholar 

  • Liao HC, Xu ZS (2014b) Satisfaction degree based interactive decision making method under hesitant fuzzy environment with incomplete weights. Int J Uncertainty Fuzziness Knowl-Based Syst 22(4):553–572

    Article  Google Scholar 

  • Liao HC, Xu ZS (2015a) Extended hesitant fuzzy hybrid weighted aggregation operators and their application in decision making. Soft Comput 19(9):2551–2564

    Article  Google Scholar 

  • Liao HC, Xu ZS (2015b) Approaches to manage hesitant fuzzy linguistic information based on the cosine distance and similarity measures for HFLTSs and their application in qualitative decision making. Expert Syst Appl 42:5328–5336

    Article  Google Scholar 

  • Liao HC, Xu ZS, Xia MM (2014a) Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making. Int J Inf Technol Decis Making 13(1):47–76

    Article  Google Scholar 

  • Liao HC, Xu ZS, Zeng XJ (2014b) Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making. Inf Sci 271:125–142

    Article  Google Scholar 

  • Liao HC, Xu ZS, Zeng XJ, Merigó JM (2015a) Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets. Knowl-Based Syst 76:127–138

    Article  Google Scholar 

  • Liao HC, Xu ZS, Zeng XJ (2015b) Novel correlation coefficients between hesitant fuzzy sets and their application in decision making. Knowl-Based Syst 82:115–127

    Article  Google Scholar 

  • Liao HC, Xu ZS, Zeng XJ (2015c) Hesitant fuzzy linguistic VIKOR method and its application in qualitative multiple criteria decision making. IEEE Trans Fuzzy Syst 23(5):1343–1355

    Article  Google Scholar 

  • Mizumoto M, Tanaka K (1976) Some properties of fuzzy sets of type 2. Inf Control 31:312–340

    Article  Google Scholar 

  • Rodríguez RM, Martínez L, Herrera F (2012) Hesitant fuzzy linguistic terms sets for decision making. IEEE Trans Fuzzy Syst 20(1):109–119

    Article  Google Scholar 

  • Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25:529–539

    Google Scholar 

  • Torra V, Narukawa Y (2009) On hesitant fuzzy sets and decision. The 18th IEEE international conference on fuzzy systems (FS’09). Jeju Island, Korea, pp 1378–1382

    Chapter  Google Scholar 

  • Türkşen IB (2002) Type 2 representation and reasoning for CWW. Fuzzy Sets Syst 127:17–36

    Article  Google Scholar 

  • Wang JH, Hao J (2006) A new version of 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 14:435–445

    Article  Google Scholar 

  • Xia MM, Xu ZS (2011a) Hesitant fuzzy information aggregation in decision making. Int J Approximate Reasoning 52(3):395–407

    Article  Google Scholar 

  • Xia MM, Xu ZS (2011b) Methods for fuzzy complementary preference relations based on multiplicative consistency. Comput Ind Eng 61(4):930–935

    Article  Google Scholar 

  • Xu ZS (2004) A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Inf Sci 166:19–30

    Article  Google Scholar 

  • Xu ZS (2005) Deviation measures of linguistic preference relations in group decision making. Omega-Int J Manage Sci 33:249–254

    Article  Google Scholar 

  • Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15:1179–1187

    Article  Google Scholar 

  • Xu ZS, Da QL (2002) The uncertain OWA operator. Int J Intell Syst 17:569–575

    Article  Google Scholar 

  • Xu ZS, Xia MM (2011a) Distance and similarity measures for hesitant fuzzy sets. Inf Sci 181:2128–2138

    Article  Google Scholar 

  • Xu ZS, Xia MM (2011b) On distance and correlation measures of hesitant fuzzy information. Int J Intell Syst 26:410–425

    Article  Google Scholar 

  • Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35:417–433

    Article  Google Scholar 

  • Yager RR (1986) On the theory of bags. Int J Gen Syst 13:23–37

    Article  Google Scholar 

  • Yager RR (2014) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965

    Article  Google Scholar 

  • Yu PL (1973) A class of solutions for group decision problems. Manage Sci 19:936–946

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  Google Scholar 

  • Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-I. Inf Sci 8:199–249

    Article  Google Scholar 

  • Zhao N, Xu ZS, Liu FJ (2015) Uncertainty measures for hesitant fuzzy information. Int J Intell Syst 30(7):818–836

    Article  Google Scholar 

  • Zhao H, Xu ZS, Liu SS (2016) Dual hesitant fuzzy information aggregation with Einstein t-conorm and t-norm. J Syst Sci Syst Eng. doi:10.1007/s11518-015-5289-6

    Google Scholar 

  • Zhu B, Xu ZS, Xia MM (2012) Dual hesitant fuzzy set. J Appl Math 879629, 13 p. doi:10.1155/2012/879629

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Authors and Affiliations

  1. Business School, Sichuan University, 29 Wangjiang Road, Chengdu, Sichuan, China

    Huchang Liao & Zeshui Xu

Authors
  1. Huchang Liao
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  2. Zeshui Xu
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Correspondence to Huchang Liao .

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© 2017 Springer Nature Singapore Pte Ltd.

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Liao, H., Xu, Z. (2017). Hesitant Fuzzy Set and Its Extensions. In: Hesitant Fuzzy Decision Making Methodologies and Applications . Uncertainty and Operations Research. Springer, Singapore. https://doi.org/10.1007/978-981-10-3265-3_1

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