Skip to main content
Log in

Multi-criteria outranking approach with hesitant fuzzy sets

  • Regular Article
  • Published:
OR Spectrum Aims and scope Submit manuscript

Abstract

As a generalization of fuzzy sets, hesitant fuzzy sets constrain the membership degree of an element to be a set of possible values between zero and one. Those sets are considered useful in handling decision problems defined under uncertainties where decision-makers hesitate among several values before expressing their preferences. Motivated by the idea of traditional ELECTRE methods, the dominance relations and the opposition relations for hesitant fuzzy sets are introduced in this paper. In addition, several desirable properties are studied. Then, a novel outranking relation is developed, based on systematic comparison of assessments given to alternatives for each criterion. An outranking approach for multi-criteria decision-making problems with hesitant fuzzy sets, similar to ELECTRE III, is proposed for ranking alternatives. Finally, an example is given to verify the developed approach and demonstrate its validity and feasibility.

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

Access this article

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

  • 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 Manage 30:870–879

    Article  Google Scholar 

  • Akram M, Dudek WA (2013) Intuitionistic fuzzy hypergraphs with applications. Inf Sci 218:182–193

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Atanassov KT (1989) More on intuitionistic fuzzy sets. Fuzzy Sets Syst 33:37–45

    Article  Google Scholar 

  • Atanassov KT (1999) Intuitionistic fuzzy sets. Springer, Heidelberg

    Book  Google Scholar 

  • Atanassov KT (2000) Two theorems for intuitionistic fuzzy sets. Fuzzy Sets Syst 110:267–269

    Article  Google Scholar 

  • Beliakov G, Pradera A, Calvo T (2007) Aggregation functions: a guide for practitioners. Springer, Heidelberg

    Google Scholar 

  • Bellman R, Zadeh LA (1990) Decision making in a fuzzy environment. Manage Sci 17:141–164

    Article  Google Scholar 

  • Bojković N, Anić I, Pejčić-Tarle S (2010) One solution for cross-country transport-sustainabilityevaluation using a modified ELECTRE method. Ecol Econ 69:1176–1186

    Article  Google Scholar 

  • Cavallaro F (2010) A comparative assessment of thin-film photovoltaic production processes using the ELECTRE III method. Energy Policy 38:463–474

    Article  Google Scholar 

  • Chen TY (2011) A comparative analysis of score functions for multiple criteria decision making in intuitionistic fuzzy settings. Inf Sci 181:3652–3676

    Article  Google Scholar 

  • Chen ZP, Yang W (2012) A new multiple criteria decision making method based on intuitionistic fuzzy information. Expert Syst Appl 39:4328–4334

    Article  Google Scholar 

  • Chen N, Xu ZS, Xia MM (2013a) Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl Math Model 37:2197–2221

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Devi K, Yadav SP (2013) A multicriteria intuitionistic fuzzy group decision making for plant location selection with ELECTRE method. Int J Adv Manuf Technol 66:1219–1229

    Article  Google Scholar 

  • Ermatita Hartati S, Wardoyo R, Harjoko A (2011) ELECTRE methods in solving group decision support system bioinformatics on gene mutation detection simulation. Int J Comput Sci Inf Technol 3:40–52

    Google Scholar 

  • Farhadinia B (2013a) A novel method of ranking hesitant fuzzy values for multiple attribute decision-making problems. Int J Intell Syst 28(8):752–767

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Figueira JR, Almeida-Dias J, Matiasd S et al (2011) Electre Tri-C, a multiple criteria decision aiding sorting model applied to assisted reproduction. Int J Med Inform 80:262–273

    Google Scholar 

  • 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 101:555–561

    Article  Google Scholar 

  • 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 39:676–688

    Article  Google Scholar 

  • Kaya T, Kahraman C (2011) An integrated fuzzy AHP-ELECTRE methodology for environmental impact assessment. Expert Syst Appl 38:8553–8562

    Article  Google Scholar 

  • Klement EP, Mesiar R (2005) Logical, algebraic, analytic, and probabilistic aspects of triangular norms. Elsevier, New York

    Google Scholar 

  • Liao HC, Xu ZS (2013) A VIKOR-based method for hesitant fuzzy multi-criteria decision making. Fuzzy Optim Decis Making. doi:10.1007/s10700-013-9162-0

    Google Scholar 

  • Marzouk MM (2011) ELECTRE III model for value engineering applications. Autom Constr 20:596–600

    Article  Google Scholar 

  • Mukherjee S, Basu K (2012) Solution of a class of intuitionistic fuzzy assignment problem by using similarity measures. Knowl-Based Syst 27:170–179

    Article  Google Scholar 

  • Nguyen HT, Walker RA (1997) A first course in fuzzy logic. CRC press, Boca Raton

    Google Scholar 

  • 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 38:9773–9779

    Article  Google Scholar 

  • Paternain D, Jurio A, Barrenechea E et al (2012) An alternative to fuzzy methods in decision-making problems. Expert Syst Appl 39:7729–7735

    Article  Google Scholar 

  • Pedrycz W (1990) Fuzzy sets in pattern recognition: methodology and methods. Pattern Recognit 23:121–146

    Article  Google Scholar 

  • Pekala B (2012) Properties of Atanassov’s intuitionistic fuzzy relationsand Atanassov’s operators. Inf Sci 213:84–93

    Article  Google Scholar 

  • Peng DH, Gao CY, Gao ZF (2013) Generalized hesitant fuzzy synergetic weighted distance measures and their application to multiple criteria decision-making. Appl Math Model 37:5837–5850

    Article  Google Scholar 

  • Qian G, Wang H, Feng XQ (2013) Generalized hesitant fuzzy sets and their application in decision support system. Knowl-Based Syst 37:357–365

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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 3:43–65

    Article  Google Scholar 

  • Tan CQ, Chen XH (2010) Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making. Expert Syst Appl 37:149–157

    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. 18th IEEE Int Conf Fuzzy Syst, Jeju Island, Korea, pp 1378–1382

  • Verma R, Sharma BD (2013) New operations over hesitant fuzzy sets. Fuzzy Inf Eng 5(1):129–146

    Article  Google Scholar 

  • Wei GW (2010) Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making. Appl Soft Comput 10:423–431

    Article  Google Scholar 

  • Wei GW (2011) Gray relational analysis method for intuitionistic fuzzy multiple attribute decision making. Expert Syst Appl 38:11671–11677

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Wei GW, Zhao XF (2012) Some induced correlated aggregating operators with intuitionistic fuzzy information and their application to multiple attribute group decision making. Expert Syst Appl 39:2026–2034

    Article  Google Scholar 

  • 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 24:789–803

    Google Scholar 

  • 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 

  • Xia MM (2012) Research on fuzzy decision information aggregation techniques and measures. Southeast University, Dissertation

    Google Scholar 

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

    Article  Google Scholar 

  • Xia MM, Xu ZS, Zhu B (2012) Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm. Knowl-Based Syst 31:78–88

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Xu ZS (2011) Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators. Knowl-Based Syst 24:749–760

    Article  Google Scholar 

  • Xu ZS (2012) An error-analysis-based method for the priority of an intuitionistic preference relation in decision making. Knowl-Based Syst 33:173–179

    Article  Google Scholar 

  • 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 

  • Xu ZS, Xia MM (2011a) Induced generalized intuitionistic fuzzy operators. Knowl-Based Syst 24:197–209

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Yager RR (1997) Multiple objective decision-making using fuzzy sets. Int J Man-Mach Stud 9:375–382

    Google Scholar 

  • Yu XH, Xu ZS (2013) Prioritized intuitionistic fuzzy aggregation operators. Inf Fusion 14:108–116

    Article  Google Scholar 

  • Yu DJ, Zhang WY (2013) Group decision making under hesitant fuzzy environment with application to personnel evaluation. Knowl-Based Syst 52:1–10

    Article  Google Scholar 

  • Yu DJ, Wu YY, Zhou W (2011) Multi-criteria decision making based on Choquet integral under hesitant fuzzy environment. J Comput Inf Syst 7(12):4506–4513

    Google Scholar 

  • Yue J (2010) Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment. Eur J Oper Res 205:202–204

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–356

    Article  Google Scholar 

  • Zadeh LA (1975) Fuzzy logic and approximate reasoning. Synthese 30:407–428

    Article  Google Scholar 

  • Zeng SZ, Su WH (2011) Intuitionistic fuzzy ordered weighted distance operator. Knowl-Based Syst 24:1224–1232

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

Download references

Acknowledgments

The authors thank the editors and anonymous reviewers for their helpful comments and suggestions. This work was supported by the National Natural Science Foundation, P.R. China (Nos. 71271218 and 71221061).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jian Qiang Wang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, J.Q., Wang, D.D., Zhang, H.y. et al. Multi-criteria outranking approach with hesitant fuzzy sets. OR Spectrum 36, 1001–1019 (2014). https://doi.org/10.1007/s00291-013-0354-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00291-013-0354-3

Keywords

Navigation