Skip to main content
SpringerLink
Log in

Multi-criteria decision-making using interval-valued hesitant fuzzy QUALIFLEX methods based on a likelihood-based comparison approach

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

QUALIFLEX is a very efficient outranking method to handle multi-criteria decision-making (MCDM) involving cardinal and ordinal preference information. Based on a likelihood-based comparison approach, this paper develops two interval-valued hesitant fuzzy QUALIFLEX outranking methods to handle MCDM problems within the interval-valued hesitant fuzzy context. First, we define the likelihoods of interval-valued hesitant fuzzy preference relations that compare two interval-valued hesitant fuzzy elements (IVHFEs). Then, we propose the concepts of the concordance/discordance index, the weighted concordance/discordance index and the comprehensive concordance/discordance index. Moreover, an interval-valued hesitant fuzzy QUALIFLEX model is developed to solve MCDM problems where the evaluative ratings of the alternatives and the weights of the criteria take the form of IVHFEs. Additionally, this paper propounds another likelihood-based interval-valued hesitant fuzzy QUALIFLEX method to accommodate the IVHFEs’ evaluative ratings of alternatives and non-fuzzy criterion weights with incomplete information. Finally, a numerical example concerning the selection of green suppliers is provided to demonstrate the practicability of the proposed methods, and a comparison analysis is given to illustrate the advantages of the proposed methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. Atanassov K (1989) More on intuitionistic fuzzy sets. Fuzzy Sets Syst 33:37–46

    Article  MathSciNet  MATH  Google Scholar 

  3. Atanassov KT, Gargov G (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31(3):343–349

    Article  MathSciNet  MATH  Google Scholar 

  4. Benayoun R, Roy B, Sussman N (1966) Manual de Reference du Program ELECTRE. Note de Synthese et Formation, Direction Scientifique SEMA, No. 25, Paris, 823 France

  5. Chen TY (2013) Data construction process and qualiflex-based method for multiple-criteria group decision making with interval-valued intuitionistic fuzzy sets. Int J Inf Technol Decis Mak 12:425–467

    Article  Google Scholar 

  6. Chen TY (2014) Interval-valued intuitionistic fuzzy QUALIFLEX method with a likelihood-based comparison approach for multiple criteria decision analysis. Inf Sci 261:149–169

    Article  MathSciNet  MATH  Google Scholar 

  7. Chen TY, Chang CH, Lu JFR (2013) The extended QUALIFLEX method for multiple criteria decision analysis based on interval type-2 fuzzy sets and applications to medical decision making. Eur J Oper Res 226:615–625

    Article  MathSciNet  MATH  Google Scholar 

  8. Chen TY, Tsui CW (2012) Intuitionistic fuzzy QUALIFLEX method for optimistic and pessimistic decision making. Adv Inf Sci Serv Sci 4(14):219–226

    Google Scholar 

  9. Chen TY, Wang JC (2009) Interval-valued fuzzy permutation method and experimental analysis on cardinal and ordinal evaluations. J Comput Syst Sci 75(7):371–387

    Article  MathSciNet  MATH  Google Scholar 

  10. Chen TY, Wang JC, Tsui CW (2007) Decision model with permutation methods based on intuitionistic fuzzy sets. In: Proceedings of the 8th Asia Pacific industrial engineering and management system and 2007 Chinese Institute of Industrial Engineers Conference (APIEMS and CIIE 2007), pp 243–250

  11. 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 

  12. Chen N, Xu ZS, Xia MM (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 

  13. Dyer JS, Fishburn PC, Steuer RE, Wallenius J, Zionts S (1992) Multiple criteria decision making, multiattribute utility theory: the next ten years. Manag Sci 38:645–654

    Article  MATH  Google Scholar 

  14. Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic Press, New York

    MATH  Google Scholar 

  15. Facchinetti G, Ricci RG, Muzzioli S (1998) Note on ranking fuzzy triangular numbers. Int J Intell Syst 13:613–622

    Article  Google Scholar 

  16. 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 

  17. Farhadinia B (2014) Correlation for dual hesitant fuzzy sets and dual interval-valued hesitant fuzzy sets. Int J Intell Syst 29:184–205

    Article  Google Scholar 

  18. Griffith DA, Paelinck JHP (2011) Qualireg, a qualitative regression method. Adv Geogr Inf Sci 1(2):227–233

    Article  Google Scholar 

  19. Hinloopen E, Nijkamp P, Rietveld P (2004) Integration of ordinal and cardinal information in multiple criteria ranking with imperfect compensation. Eur J Oper Res 158(2):317–338

    Article  MATH  Google Scholar 

  20. Hokkanen J, Lahdelma R, Salminen P (2000) Multicriteria decision support in a technology competition for cleaning polluted soil in Helsinki. J Environ Manag 60(4):339–348

    Article  Google Scholar 

  21. Hwang CL, Yoon K (1981) Multiple attribute decision making: methods and applications. Springer, Berlin

    Book  MATH  Google Scholar 

  22. Lahdelma R, Miettinen K, Salminen P (2003) Ordinal criteria in stochastic multicriteria acceptability analysis (SMAA). Eur J Oper Res 147(1):117–127

    Article  MATH  Google Scholar 

  23. Li DF (2011) Closeness coefficient based nonlinear programming method for interval-valued intuitionistic fuzzy multiattribute decision making with incomplete preference information. Appl Soft Comput 11(4):3402–3418

    Article  Google Scholar 

  24. Li LG, Peng DH (2014) Interval-valued hesitant fuzzy Hamacher synergetic weighted aggregation operators and their application to shale gas areas selection. Math Probl Eng 2014:1–25

    MathSciNet  Google Scholar 

  25. Martel JM, Matarazzo B (2005) Other outranking approaches. In: Figueira J, Greco S, Ehrgott M (eds) Multiple criteria decision analysis: state of the art surveys. Springer, New York, pp 197–262

    Chapter  Google Scholar 

  26. Meng FY, Wang C, Chen XH, Zhang Q (2016) Correlation coefficients of interval-valued hesitant fuzzy sets and their application based on the Shapley function. Int J Intell Syst 31(1):17–43

    Article  Google Scholar 

  27. Paelinck JHP (1976) Qualitative multiple criteria analysis, environmental protection and multiregional development. Pap Reg Sci Assoc 36(1):59–74

    Article  Google Scholar 

  28. Paelinck JHP (1977) Qualitative multicriteria analysis: an application to airport location. Environ Plan 9(8):883–895

    Article  Google Scholar 

  29. Paelinck JHP (1978) QUALIFLEX: a flexible multiple criteria method. Econ Lett 1(3):193–197

    Article  MathSciNet  Google Scholar 

  30. Park JH, Park IY, Kwun YC, Tan X (2011) Extension of the TOPSIS method for decision making problems under interval-valued intuitionistic fuzzy environment. Appl Math Model 35(5):2544–2556

    Article  MathSciNet  MATH  Google Scholar 

  31. Peng DH, Wang TD, Gao CY, Wang H (2014) Continuous hesitant fuzzy aggregation operators and their application to decision making under interval-valued hesitant fuzzy setting. Sci World J 2014:1–20

    Google Scholar 

  32. Quirós P, Alonso P, Bustince H, Díaz I, Montes S (2015) An entropy measure definition for finite interval-valued hesitant fuzzy sets. Knowl-Based Syst 84:121–133

    Article  Google Scholar 

  33. Rebai A, Aouni B, Martel J-M (2006) A multi-attribute method for choosing among potential alternatives with ordinal evaluation. Eur J Oper Res 174(1):360–373

    Article  MATH  Google Scholar 

  34. Roy B (1968) Classement et Choix en Presence de Points de vue Multiples (la method Electre). Revue Francaise d’Informatique et de Recherche Operationnelle 8:57–75

    Article  Google Scholar 

  35. Roy B (1991) The outranking approach and the foundations of ELECTRE methods. Theory Decis 31:49–73

    Article  MathSciNet  Google Scholar 

  36. Sarabando P, Dias LC (2010) Simple procedures of choice in multicriteria problems without precise information about the alternatives’ values. Comput Oper Res 37(12):2239–2247

    Article  MathSciNet  MATH  Google Scholar 

  37. Shen L, Olfat L, Govindan K, Khodaverdi R, Diabat A (2013) A fuzzy multi criteria approach for evaluating green supplier’s performance in green supply chain with linguistic preferences. Resour Conserv Recycl 74:170–179

    Article  Google Scholar 

  38. Stewart TJ (1992) A critical survey on the status of multiple criteria decision making theory and practice. Omega 20:569–586

    Article  Google Scholar 

  39. Torra V (2010) Hesitant fuzzy sets. International Journal of Intelligent Systems 25:529–539

    MATH  Google Scholar 

  40. Torra V, Narukawa Y (2009) On hesitant fuzzy sets and decision. In: The 18th IEEE international conference on fuzzy systems, Jeju Island, Korea, 707, pp 1378–1382

  41. Wang JC, Tsao CY, Chen TY (2015) A likelihood-based QUALIFLEX method with interval type-2 fuzzy sets for multiple criteria decision analysis. Soft Comput 19(8):2225–2243

    Article  Google Scholar 

  42. Wang YM, Yang JB, Xu DL (2005) A two-stage logarithmic goal programming method for generating weights from interval comparison matrices. Fuzzy Sets Syst 152:475–498

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  44. 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(2):337–349

    Article  Google Scholar 

  45. 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):789–803

    MathSciNet  MATH  Google Scholar 

  46. Wei GW, 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 

  47. 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 

  48. Xu ZS, Chen J (2008) Some models for deriving the priority weights from interval fuzzy preference relations. Eur J Oper Res 184:266–280

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  50. Xu ZS, Zhang XL (2013) Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information. Knowl-Based Syst 52:53–64

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  53. 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 67:116–138

    Article  Google Scholar 

  54. Zhang ZM, Wu C (2014) Some interval-valued hesitant fuzzy aggregation operators based on Archimedean t-norm and t-conorm with their application in multi-criteria decision making. J Intell Fuzzy Syst 27(6):2737–2748

    MathSciNet  MATH  Google Scholar 

  55. Zhang XL, Xu ZS (2015) Hesitant fuzzy QUALIFLEX approach with a signed distance-based comparison method for multiple criteria decision analysis. Expert Syst Appl 42(2):873–884

    Article  MathSciNet  Google Scholar 

  56. Zhu QH, Sarkis J (2004) Relationships between operational practices and performance among early adopters of green supply chain management practices in Chinese manufacturing enterprises. J Oper Manag 22:265–289

    Article  Google Scholar 

  57. Zimmermann HJ, Zysno P (1980) Latent connectives in human decision making. Fuzzy Sets Syst 4(1):37–51

    Article  MATH  Google Scholar 

Download references

Acknowledgments

The author thanks the anonymous referees for their valuable suggestions in improving this paper. This work is supported by the National Natural Science Foundation of China (Grant No. 61375075) and the Natural Science Foundation of Hebei Province of China (Grant No. F2012201020).

Author information

Authors and Affiliations

  1. College of Mathematics and Information Science, Hebei University, Baoding, 071002, Hebei, China

    Zhiming Zhang

Authors
  1. Zhiming Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhiming Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, Z. Multi-criteria decision-making using interval-valued hesitant fuzzy QUALIFLEX methods based on a likelihood-based comparison approach. Neural Comput & Applic 28, 1835–1854 (2017). https://doi.org/10.1007/s00521-015-2156-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-015-2156-9

Keywords

Search

Navigation