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Soft Computing

, Volume 21, Issue 12, pp 3439–3459 | Cite as

Hesitant fuzzy multi-attribute decision-making based on the minimum deviation method

  • Hua Zhao
  • Zeshui XuEmail author
  • Hai Wang
  • Shousheng Liu
Methodologies and Application

Abstract

As a powerful and efficient tool in expressing the indeterminate and fuzzy information, the hesitant fuzzy set (HFS) has shown its increasing importance. It was first proposed by Torra and Narukawa, permitting the membership degree of an element to a set of several possible values. In this paper, based on the idea of minimum deviation between the subjective and the objective preferences, we first develop two methods to determine the attribute weights under the hesitant fuzzy environment. To do so, we present the concept of hesitant fuzzy expected value and then establish several optimization models to gain the attribute weights. After that, we use the information aggregation techniques to integrate the hesitant fuzzy attribute values or their expected values, and then sort the alternatives by the overall values. Moreover, we generalize these two methods to interval-valued HFSs, and a numerical example is utilized to show the detailed implementation procedure and effectiveness of our methods in solving multi-attribute decision-making problems with hesitant fuzzy or interval-valued hesitant fuzzy information.

Keywords

Hesitant fuzzy set Multi-attribute decision-making  Minimum deviation Weight 

Notes

Acknowledgments

The work was supported by the National Natural Science Foundation of China (No. 61273209) and the Central University Basic Scientific Research Business Expenses Project (No. skgt201501).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. Bedregal B, Beliakov G, Bustince H, Calvo T, Mesiar R, Paternain D (2012) A class of fuzzy multisets with a fixed number of memberships. Inf Sci 189:1–17MathSciNetCrossRefzbMATHGoogle Scholar
  2. Bellmanhe RE, Zadeh LA (1970) Decision-making in a fuzzy environment. Manag Sci 17:141–164MathSciNetCrossRefGoogle Scholar
  3. Cao QW, Wu J (2011) The extended COWG operators and their application to multiple attributive group decision making problems with interval numbers. Appl Math Model 35:2075–2086MathSciNetCrossRefzbMATHGoogle Scholar
  4. Cevik Onar S, Oztaysi B, Kahraman C (2014) Strategic decision selection using hesitant fuzzy TOPSIS and interval type-2 fuzzy AHP: a case study. Int J Comput Intell Syst 7:1002–1021CrossRefGoogle Scholar
  5. Chang JR, Ho TH, Cheng CH, Chen AP (2006) Dynamic fuzzy OWA model for group multiple criteria decision making. Soft Comput 10:543–554CrossRefGoogle Scholar
  6. Chen SJ, Hwang CL (1992) Fuzzy multiple attribute decision making: methods and applications. Springer, BerlinCrossRefzbMATHGoogle Scholar
  7. Chen N, Xu ZS, Xia MM (2013) Interval-valued hesitant preference relations and their applications to group decision making. Knowl-Based Syst 37:528–540CrossRefGoogle Scholar
  8. Hwang CL, Yoon K (1981a) Multiple attribute decision making. In: Lecture Notes in Economics and Mathematical Systems. Springer, Berlin, p 186Google Scholar
  9. Hwang CL, Yoon K (1981b) Multiple attribute decision making. Springer, Berlin, Heidelberg, New YorkGoogle Scholar
  10. Jiang BC, Hsu CH (2003) Development of a fuzzy decision model for manufacturability evaluation. J Intell Manuf 14:169–181CrossRefGoogle Scholar
  11. Li DF (2007) A fuzzy closeness approach to fuzzy multi-attribute decision making. Fuzzy Optim Decis Mak 6:237–254MathSciNetCrossRefzbMATHGoogle Scholar
  12. Liao HC, Xu ZS (2014a) Some new hybrid weighted aggregation operators under hesitant fuzzy multi-criteria decision making environment. J Intell Fuzzy Syst 26:1601–1617Google Scholar
  13. 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 22:553–572Google Scholar
  14. 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 13:47–76CrossRefGoogle Scholar
  15. Mousavi SM, Jolai F, Tavakkoli-Moghaddam R, Fuzzy A (2013) Stochastic multi-attribute group decision-making approach for selection problems. Group Decis Negot 22:207–233CrossRefGoogle Scholar
  16. Opricovic S (2011) Fuzzy VIKOR with an application to water resources planning. Expert Syst Appl 38:12983–12990CrossRefGoogle Scholar
  17. Park JH, Cho HJ, Kwun YC (2011) Extension of the VIKOR method for group decision making with interval-valued intuitionistic fuzzy information. Fuzzy Optim Decis Mak 10:233–253MathSciNetCrossRefzbMATHGoogle Scholar
  18. Rao RV, Davim JP (2008) A decision-making framework model for material selection using a combined multiple attribute decision-making method. Int J Adv Manuf Technol 35:751–760CrossRefGoogle Scholar
  19. Rodríguez RM, Martínez L, Herrera F (2012) Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst 20:109–119CrossRefGoogle Scholar
  20. Rodríguez RM, Martínez L, Herrera F (2013) A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets. Inf Sci 241:28–42MathSciNetCrossRefzbMATHGoogle Scholar
  21. Rodríguez RM, Martínez L, Torra V, Xu ZS (2014) Hesitant fuzzy sets: state of the art and future direction. Int J Intell Syst 29:495–524CrossRefGoogle Scholar
  22. Su ZX, Xia GP, Chen MY, Wang L (2012) Induced generalized intuitionistic fuzzy OWA operator for multi-attribute group decision making. Expert Syst Appl 39:1902–1910CrossRefGoogle Scholar
  23. Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25:529–539zbMATHGoogle Scholar
  24. Torra V, Narukawa Y (2009) On hesitant fuzzy sets and decision. In: The 18th IEEE international conference on fuzzy systems, Jeju Island, Korea, pp 1378–1382Google Scholar
  25. Wang YM (1998) Using the method of maximizing deviations to make decision for multi-indices. Syst Eng Electron 7(24–26):31Google Scholar
  26. Wei GW, Wang HJ, Lin R (2011) Application of correlation coefficient to interval-valued intuitionistic fuzzy multiple attribute decision-making with incomplete weight information. Knowl Inf Syst 26:337–349CrossRefGoogle Scholar
  27. Xia MM, Xu ZS (2011) Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 52:395–407MathSciNetCrossRefzbMATHGoogle Scholar
  28. Xia MM, Xu ZS, Chen N (2013) Some hesitant fuzzy aggregation operators with their application in group decision making. Group Decis Negot 22:259–279CrossRefGoogle Scholar
  29. Xu ZS (2004) Method based on expected values for fuzzy multiple attribute decision making problems with preference information on alternatives. Syst Eng-Theory Pract 1(109–113):119Google Scholar
  30. Xu ZS (2007) Intuitionistic preference relations and their application in group decision making. Inf Sci 177:2363–2379MathSciNetCrossRefzbMATHGoogle Scholar
  31. Xu ZS, Da QL (2002) The uncertain OWA operator. Int J Intell Syst 17:569–575CrossRefzbMATHGoogle Scholar
  32. Xu ZS, Chen Q (2011) A multi-criteria decision making procedure based on interval-valued intuitionistic fuzzy Bonferroni means. J Syst Sci Syst Eng 20:217–228CrossRefGoogle Scholar
  33. Xu ZS, Xia MM (2011) Distance and similarity measures for hesitant fuzzy sets. Inf Sci 181:2128–2138MathSciNetCrossRefzbMATHGoogle Scholar
  34. Xu ZS, Zhang XL (2013) Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information. Knowl-Based Syst 52:53–64CrossRefGoogle Scholar
  35. Yang L, Deuse J, Jiang PY (2013) Multiple-attribute decision-making approach for an energy-efficient facility layout design. Int J Adv Manuf Technol 66:795–807CrossRefGoogle Scholar
  36. Yavuz M, Oztaysi B, Cevik Onar S, Kahraman C (2015) Multi-criteria evaluation of alternative-fuel vehicles via a hierarchical hesitant fuzzy linguistic model. Expert Syst Appl 42:2835–2848Google Scholar
  37. Yoon KP, Hwang CL (1996) Multiple attribute decision making—an introduction. Sage University Paper, Sage QASS Series, Sage Publications, International Educational and Professional PublisherGoogle Scholar
  38. Zadeh LA (1965) Fuzzy sets. Inf. Control 8:338–356MathSciNetCrossRefzbMATHGoogle Scholar
  39. Zhang X, Liu PD (2010) Method for multiple attribute decision-making under risk with interval numbers. Int J Fuzzy Syst 12:237–242Google Scholar
  40. Zhang XM, Xu ZS (2012) A new method for ranking intuitionistic fuzzy values and its application in multi-attribute decision making. Fuzzy Optim Decis Mak 11:135–146MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institute of SciencesPLA University of Science and TechnologyNanjingChina
  2. 2.Business SchoolSichuan UniversityChengduChina
  3. 3.School of Economics and ManagementSoutheast UniversityNanjingChina

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