Soft Computing

, Volume 23, Issue 2, pp 419–430 | Cite as

Outranking approach for multi-criteria decision-making problems with hesitant interval-valued fuzzy sets

  • Jian-qiang WangEmail author
  • Juan-juan Peng
  • Hong-yu Zhang
  • Xiao-hong Chen
Methodologies and Application


For decision makers, expressing their opinions through subintervals of [0, 1] is sometimes easier than using crisp numbers. This study defines some outranking relations derived by ELECTRE III for hesitant interval-valued fuzzy sets (HIVFSs). The properties of these outranking relations are discussed in detail. The concordance and discordance indexes of HIVFSs are then proposed. Ranking approach is developed based on the outranking relations of HIVFSs to handle multi-criteria decision-making problems. Finally, we provide practical examples, as well as sensitivity analysis and comparison with other techniques.


Multi-criteria decision-making Hesitant interval-valued fuzzy sets Outranking relations of hesitant interval-valued fuzzy sets Outranking approach 



The author would like to thank the editors and the anonymous referees for their valuable and constructive comments and suggestions that greatly help the improvement of this paper. This work was supported by the National Natural Science Foundation of China (Nos. 71571193 and 71701065) and the China Postdoctoral Science Foundation (No. 2017M610511).

Compliance with Ethical Standards

Conflict of interest

No potential conflict of interest was reported by the authors.


  1. Achillas C, Vlachokostas C, Moussiopoulos N, Banias G (2010) Decision support system for the optimal location of electrical and electronic waste treatment plants: a case study in Greece. Waste Manag 30(5):870–879CrossRefGoogle Scholar
  2. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96CrossRefzbMATHGoogle Scholar
  3. Bellman R, Zadeh LA (1970) Decision making in a fuzzy environment. Manag Sci 17:141–164MathSciNetCrossRefzbMATHGoogle Scholar
  4. Bojković N, Anić I, Pejčić-Tarle S (2010) One solution for cross-country transport-sustainability evaluation using a modified ELECTRE method. Ecol Econ 69(5):1176–1186CrossRefGoogle Scholar
  5. Cao Y, Zhou H, Wang J (2016) An approach to interval-valued intuitionistic stochastic multi-criteria decision-making using set pair analysis. Int J Mach Learn Cybern. doi: 10.1007/s13042-016-0589-9 Google Scholar
  6. Cavallaro F (2010) A comparative assessment of thin-film photovoltaic production processes using the ELECTRE III method. Energy Policy 38(1):463–474CrossRefGoogle 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. Devi K, Yadav SP (2013) A multicriteria intuitionistic fuzzy group decision making for plant location selection with ELECTRE method. Int J Adv Manuf Technol 66(9):1219–1229CrossRefGoogle Scholar
  9. Farhadinia B (2014a) Correlation for dual hesitant fuzzy sets and dual interval-valued hesitant fuzzy sets. Int J Intell Syst 29:184–205CrossRefGoogle Scholar
  10. Farhadinia B (2014b) Distance and similarity measures for higher order hesitant fuzzy sets. Knowl Based Syst 55:43–48CrossRefzbMATHGoogle Scholar
  11. Figueira JR, Almeida-Dias J, Matias S, Roy B, Carvalho MJ, Plancha CE (2011) Electre Tri-C, a multiple criteria decision aiding sorting model applied to assisted reproduction. Int J Med Inform 80(4):262–273CrossRefGoogle Scholar
  12. Hanandeh AE, El-Zein A (2010) The development and application of multi-criteria decision-making tool with consideration of uncertainty: the selection of a management strategy for the bio-degradable fraction in the municipal solid waste. Bioresour Technol 101(2):555–561CrossRefGoogle Scholar
  13. Hartati S, Wardoyo R, Harjoko A, Palembang-prabumulih J, Ilir O (2011) Electre methods in solving group decision support system bioinformatics on gene mutation detection simulation. Int J Comput Sci Inf Technol 3(1):40–52Google Scholar
  14. Haurant P, Oberti P, Muselli M (2011) Multicriteria selection aiding related to photovoltaic plants on farming fields on Corsica island: a real case study using the ELECTRE outranking framework. Energy Policy 39(2):676–688CrossRefGoogle Scholar
  15. Hokkanen J, Salminen P (1997) ELECTRE III and IV decision aids in an environmental problem. J Multi Criteria Decis Anal 6(4):215–226CrossRefzbMATHGoogle Scholar
  16. Hu BQ (2016) Three-way decision spaces based on partially ordered sets and three-way decisions based on hesitant fuzzy sets. Knowl Based Syst 91:16–31CrossRefGoogle Scholar
  17. Hu JH, Yang Y, Chen XH (2017) A novel TODIM method based three-way decision model for medical treatment selection. Int J Fuzzy Syst. doi: 10.1007/s40815-017-0320-3 Google Scholar
  18. Ji P, Zhang HY, Wang JQ (2017) Fuzzy decision-making framework for treatment selection based on the combined QUALIFLEX-TODIM method. Int J Syst Sci. doi: 10.1080/00207721.2017.1357779 zbMATHGoogle Scholar
  19. Jin FF, Ni ZW, Chen HY, Li YP, Zhou LG (2016) Multiple attribute group decision making based on interval-valued hesitant fuzzy information measures. Comput Ind Eng 101:103–115CrossRefGoogle Scholar
  20. Kaya T, Kahraman C (2011) An integrated fuzzy AHP-ELECTRE methodology for environmental impact assessment. Expert Syst Appl 38(7):8553–8562CrossRefGoogle Scholar
  21. Li J, Wang JQ (2017) Multi-criteria outranking methods with hesitant probabilistic fuzzy sets. Cognit Comput. doi: 10.1007/s12559-017-9476-2 Google Scholar
  22. Marzouk MM (2011) ELECTRE III model for value engineering applications. Autom Constr 20(5):596–600CrossRefGoogle Scholar
  23. Ozcan T, Celebi N, Esnaf S (2011) Comparative analysis of multi-criteria decision making methodologies and implementation of a warehouse location selection problem. Expert Syst Appl 38(8):9773–9779CrossRefGoogle Scholar
  24. Pedrycz W (1990) Fuzzy sets in pattern recognition: methodology and methods. Pattern Recogn 23:121–146CrossRefGoogle Scholar
  25. Peng HG, Zhang HY, Wang JQ (2016) Probability multi-valued neutrosophic sets and its application in multi-criteria group decision-making problems. Neural Comput Appl. doi: 10.1007/s00521-016-2702-0 Google Scholar
  26. Peng JJ, Wang JQ, Wu XH, Tian C (2017a) Hesitant intuitionistic fuzzy aggregation operators based on the archimedean t-norms and t-conorms. Int J Fuzzy Syst 19(3):702–714CrossRefGoogle Scholar
  27. Peng JJ, Wang JQ, Yang LJ, Qian J (2017b) A novel multi-criteria group decision-making approach using simplified neutrosophic information. Int J Uncertain Quantif 7(4):355–376CrossRefGoogle Scholar
  28. Qian G, Wang H, Feng XQ (2013) Generalized hesitant fuzzy sets and their application in decision support system. Knowl Based Syst 37:357–365CrossRefGoogle Scholar
  29. Roy B (1991) The outranking approach and the foundations of ELECTRE methods. Theor Decis 31(1):49–73MathSciNetCrossRefGoogle Scholar
  30. Sambuc R (1975) Fonctions phi-:oues, Application a l’Aide au diagnostic en pathologie thyroidienne, Ph.D. thesis, University o f Marseille, FranceGoogle Scholar
  31. Sawadogo M, Anciaux D (2011) Intermodal transportation within the green supply chain: an approach based on ELECTRE method. Int J Bus Perform Supply Chain Model 3(1):43–65CrossRefGoogle Scholar
  32. Singh PK, Kumar CA, Li JH (2016) Knowledge representation using interval-valued fuzzy formal concept lattice. Soft Comput 20(4):1485–1502CrossRefzbMATHGoogle Scholar
  33. Smarandache F (1998) Neutrosophy: neutrosophic probability, set and logic. American Research Press, Rehoboth, pp 1–105zbMATHGoogle Scholar
  34. Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25(6):529–539zbMATHGoogle Scholar
  35. 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
  36. Vallée D, Zielniewicz P (1994) ELECTRE III-IV, version 3.x-Aspects méthodologiques. Université de Paris-Dauphine, Document du LAMSADE no 85Google Scholar
  37. Wang JQ, Wang DD, Zhang HY, Chen XH (2014) Multi-criteria outranking approach with hesitant fuzzy sets. OR Spectr 36:1001–1019MathSciNetCrossRefzbMATHGoogle Scholar
  38. Wei GW, Zhao XF (2013) Induced hesitant interval-valued fuzzy Einstein aggregation operators and their application to multiple attribute decision making. J Intell Fuzzy Syst 24(4):789–803MathSciNetzbMATHGoogle Scholar
  39. Wei GW, Zhao X, Lin R (2013) Some hesitant interval-valued fuzzy aggregation operators and their applications to multiple attribute decision making. Knowl Based Syst 46:43–53CrossRefGoogle Scholar
  40. Wang J, Wang JQ, Tian ZP, Zhao DY (2017) A multi-hesitant fuzzy linguistic multi-criteria decision-making approach for logistics outsourcing with incomplete weight information. Int Trans Oper Res. doi: 10.1111/itor.12448 Google Scholar
  41. Xia MM, Xu ZS, Chen N (2013) Some Hesitant fuzzy aggregation operators with their application in group decision making. Group Decis Negot 22(2):259–279CrossRefGoogle Scholar
  42. Xu ZS (2001) Algorithm for priority of fuzzy complementary judgment matrix. J Syst Eng 16(4):311–314Google Scholar
  43. Yager RR (1997) Multiple objective decision-making using fuzzy sets. Int J Man Mach Stud 9:375–382CrossRefzbMATHGoogle Scholar
  44. Yu DJ, Wu YY, Zhou W (2011) Multi-criteria decision making based on Choquet integral under hesitant fuzzy environment. J Comput Inf Syst 12(7):4506–4513Google Scholar
  45. Yu SM, Wang J, Wang JQ (2016) An extended TODIM approach with intuitionistic linguistic numbers. Int Trans Oper Res. doi: 10.1111/itor.12363 zbMATHGoogle Scholar
  46. Yu SM, Zhang HY, Wang JQ (2017) Hesitant fuzzy linguistic maclaurin symmetric mean operators and their applications to multi-criteria decision-making problem. Int J Intell Syst. doi: 10.1002/int.21907 Google Scholar
  47. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–356CrossRefzbMATHGoogle Scholar
  48. Zadeh LA (1975) Fuzzy logic and approximate reasoning. Synthese 30:407–428CrossRefzbMATHGoogle Scholar
  49. Zhang N, Wei GW (2013) Extension of VIKOR method for decision making problem based on hesitant fuzzy set. Appl Math Model 37(7):4938–4947MathSciNetCrossRefzbMATHGoogle Scholar
  50. Zhang XL, Xu ZS (2014) The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment. Knowl Based Syst 61:48–58CrossRefGoogle Scholar
  51. Zhang ZM, Wang C, Tian DZ, Li K (2014) Induced generalized hesitant fuzzy operators and their application to multiple attribute group decision making. Comput Ind Eng 67:116–138CrossRefGoogle Scholar
  52. Zhou W (2014) An Accurate method for determining hesitant fuzzy aggregation operator weights and its application to project investment. Int J Intell Syst 29(7):668–686CrossRefGoogle Scholar
  53. Zhou H, Wang JQ, Zhang HY (2016) Stochastic multi-criteria decision-making approach based on SMAA-ELECTRE with extended grey numbers. Int Trans Oper Res. doi: 10.1111/itor.12380 Google Scholar
  54. Zhu B, Xu ZS, Xia MM (2011) Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 52(3):395–407MathSciNetCrossRefzbMATHGoogle Scholar
  55. Zhu B, Xu ZS, Xia MM (2012) Dual Hesitant Fuzzy Sets. J Appl Math 11:2607–2645MathSciNetzbMATHGoogle Scholar
  56. Zhu JQ, Fu F, Yin KX, Luo JQ, Wei D (2014) Approaches to multiple attribute decision making with hesitant interval-valued fuzzy information under correlative environment. J Intell Fuzzy Syst 27:1057–1065MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Jian-qiang Wang
    • 1
    Email author
  • Juan-juan Peng
    • 1
    • 2
  • Hong-yu Zhang
    • 1
  • Xiao-hong Chen
    • 1
  1. 1.School of BusinessCentral South UniversityChangshaChina
  2. 2.School of Economics and ManagementHubei University of Automotive TechnologyShiyanChina

Personalised recommendations