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Hesitant interval-valued fuzzy sets: some new results

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Abstract

Hesitant interval-valued fuzzy set is an extension of hesitant fuzzy set. It permits the membership degree of an element to a set to be represented as several possible interval numbers. The study of hesitant interval-valued fuzzy sets has opened a new area of research and applications. A number of mathematical results have been introduced and proved to enhance the applicability range of hesitant interval-valued fuzzy sets to wider areas. In this paper, we propose four new operations on hesitant interval valued fuzzy sets and study their properties and relations in details.

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References

  1. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    Article  MathSciNet  MATH  Google Scholar 

  2. Atanassov KT (1999) Intuitionistic Fuzzy Sets. Springer Physica-Verlag, Heidelberg

    Book  MATH  Google Scholar 

  3. Bai ZY (2013) Distance similarity measures for interval valued hesitant fuzzy sets and their application in multi criteria decision making. J Decis Syst 22(3):190–201

    Article  Google Scholar 

  4. Broumi S, Smarandache F (2014) New operations over interval valued intuitionistic hesitant fuzzy sets. Math Stat 2(2):62–71

    Google Scholar 

  5. Chen N, Xu ZS, Xia M (2013) Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl Math Model 37(4):2197–2211

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  8. Dubois D, Prade H (1980) Fuzzy sets systems. Academic Press, New York

    MATH  Google Scholar 

  9. Farhadinia B (2013) A novel method of ranking hesitant fuzzy values for multiple attribute decision making problems. Int J Intell Syst 28(8):1–16

    Article  Google Scholar 

  10. Farhadinia B (2013) Information measures for hesitant fuzzy sets and interval valued hesitant fuzzy sets. Inf Sci 240:129–144

    Article  MathSciNet  MATH  Google Scholar 

  11. Feng X, Zuo W, Wang J, Feng L (2014) Topsis method for hesitant fuzzy multiple attribute decision making. J Intell Fuzzy Syst 26(5):2263–2269

    MathSciNet  MATH  Google Scholar 

  12. Gu X, Wang Y, Yang B (2011) A method for hesitant fuzzy multiple attribute decision making and its application to risk investment. J Converg Inf Technol 6(6):282–287

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  14. Liao HC, Xu ZS (2014) Some new hybrid weighted aggregation operators under hesitant fuzzy multi criteria decision making environment. J Intell Fuzzy Syst 26(4):1601–1617

    MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  18. Lin R, Zhao XF, Wei GW (2014) Models for selecting an ERP system with hesitant fuzzy linguistic information. J Intell Fuzzy Syst 26(5):2155–2165

    MathSciNet  MATH  Google Scholar 

  19. Merigó JM, Gil-Lafuente AM, Yager RR (2014) An overview of fuzzy research with bibliometric indicators. Appl Soft Comput 27:420–433

    Article  Google Scholar 

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

    Article  Google Scholar 

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

  22. Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25(6):529–539

    MATH  Google Scholar 

  23. Verma R, Sharma BD (2015) Operations on hesitant fuzzy sets: some new results. J Intell Fuzzy Syst. doi:10.3233/IFS-151568

    MathSciNet  MATH  Google Scholar 

  24. Verma R, Sharma BD (2013) New operations over hesitant fuzzy sets. Fuzzy Inf Eng 5(2):129–146

    Article  MathSciNet  Google Scholar 

  25. Wang XR, Zhao ZH, Zhao XF, Wei G (2011) Model for evaluating the government archives website’s construction based on the GHFHWD measure with hesitant fuzzy information. J Digit Content Technol Appl 5(12):418–425

    Google Scholar 

  26. Wei GW, Zhao XF (2013) Induced hesitant interval-valued fuzzy Einstein aggregation operators and their applications to multiple attribute group decision making. J Intell Fuzzy Syst 24(4):789–803

    MATH  Google Scholar 

  27. Wei GW, Lin R, Wang H (2014) Distance and similarity measures on hesitant interval valued fuzzy sets. J Intell Fuzzy Syst 27(1):19–36

    MathSciNet  MATH  Google Scholar 

  28. Wei GW, Zhao XF, Lin R, Wang H (2014) 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

    MathSciNet  MATH  Google Scholar 

  29. Wei G, Zhao XF, Lin R (2013) Some hesitant interval valued fuzzy aggregation operators and their applications to multiple attribute decision making. Knowl Based Syst 46:43–53

    Article  Google Scholar 

  30. Wei GW, Zhao XF, Lin R, Wang H (2014) Approaches to hesitant fuzzy multiple attribute decision making with incomplete weight information. J Intell Fuzzy Syst 26(1):259–266

    MathSciNet  MATH  Google Scholar 

  31. Wei G, Zhao XF, Wang HJ, Lin R (2012) Hesitant fuzzy Choquet integral aggregation operators and their applications to multiple attribute decision making. Inf: Interdiscip J 15(2):441–448

    Google Scholar 

  32. Wei G (2012) Hesitant fuzzy prioritized operators and their application to multiple attribute decision making. Knowl Based Syst 31:176–182

    Article  Google Scholar 

  33. Xia MM, Xu ZS (2011) Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 52(3):395–407

    Article  MathSciNet  MATH  Google Scholar 

  34. Xia MM, Xu ZS, Chen N (2011) Induced aggregation under confidence levels. Int J Uncertainty Fuzziness Knowl-Based Syst 19(2):201–227

    Article  MathSciNet  Google Scholar 

  35. Xia MM, Xu ZS, Chen N (2013) Some hesitant fuzzy aggregation operators with their application in decision making. Group Decis Negot 22(2):259–279

    Article  Google Scholar 

  36. Xu ZS, Xia MM (2012) Hesitant fuzzy entropy measures and their use in multi attribute decision making. Int J Intell Syst 27(9):799–822

    Article  Google Scholar 

  37. Xu ZS, Xia MM (2011) Distance and similarity measures on hesitant fuzzy sets. Inf Sci 181(11):2128–2138

    Article  MathSciNet  MATH  Google Scholar 

  38. Xu ZS, Xia MM (2011) On distance and correlation measures of hesitant fuzzy information. Int J Intell Syst 26(5):410–425

    Article  MATH  Google Scholar 

  39. Xu ZS, Zhang X (2012) Hesitant fuzzy multiple attribute decision making based on TOPSIS with incomplete weight information. Knowl Based Syst 52:53–64

    Article  Google Scholar 

  40. Xu ZS, Zhang X (2014) Satisfaction degree based interactive decision making method under hesitant fuzzy environment with incomplete weights. Int J Uncertainty Fuzziness Knowledge Based Syst 22(4):533–572

    MathSciNet  Google Scholar 

  41. Yager RR (1986) On the theory of bags. Int J Gen Syst 13(1):23–37

    Article  MathSciNet  Google Scholar 

  42. Yu D, Zhang W, Xu Y (2013) Group decision making under hesitant fuzzy environment with application to personnel evaluation. Knowl Based Syst 52:1–10

    Article  Google Scholar 

  43. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  MATH  Google Scholar 

  44. Zhang N, Wei G (2013) Extension of VIKOR method for decision making problem based on hesitant fuzzy set. Appl Math Model 37(1):4938–4947

    Article  MathSciNet  Google Scholar 

  45. Zhang N, Wei G (2014) A multiple criteria hesitant fuzzy decision making with Shapley value based VIKOR method. J Intell Fuzzy Syst 26(2):1065–1075

    MathSciNet  MATH  Google Scholar 

  46. Zhang X, Xu ZS (2015) Hesitant fuzzy agglomerative hierarchical clustering algorithms. Int J Syst Sci 46(3):562–576

    Article  MathSciNet  MATH  Google Scholar 

  47. Zhang Y (2014) Models for decision making problems with hesitant fuzzy information. J Intell Fuzzy Syst 27(2):839–847

    MathSciNet  MATH  Google Scholar 

  48. Zhang ZM (2013) Hesitant fuzzy power aggregation operators and their applications to multiple attribute group decision making. Inf Sci 234:150–181

    Article  MathSciNet  MATH  Google Scholar 

  49. Zhou L, Zhao XF, Wei GW (2015) Hesitant fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. J Intell Fuzzy Syst 26:325–349

    MathSciNet  MATH  Google Scholar 

  50. Zhu B, Xu ZS (2013) Hesitant fuzzy Bonferroni means for multi criteria decision making. J Oper Res Soc 64:1831–1840

    Article  Google Scholar 

  51. Zhu B, Xu ZS, Xu J (2014) Deriving a ranking from hesitant fuzzy preference relations under group decision making. IEEE Trans Cybern 44(8):1328–1337

    Article  Google Scholar 

  52. Zhu B, Xu ZS, Xu J (2012) A MST cluster analysis method under hesitant fuzzy environment. Control Cybern 41(3):645–666

    MATH  Google Scholar 

  53. Zhu B, Xu ZS, Xia MM (2012) Hesitant fuzzy geometric Bonferroni means. Inf Sci 205(1):72–85

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Rajkumar Verma.

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Verma, R. Hesitant interval-valued fuzzy sets: some new results. Int. J. Mach. Learn. & Cyber. 8, 865–876 (2017). https://doi.org/10.1007/s13042-015-0452-4

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