Skip to main content
SpringerLink
Log in

Outranking method for intuitionistic 2-tuple fuzzy linguistic information model in group decision making

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

This paper attempts to develop an outranking method based on intuitionistic 2-tuple fuzzy linguistic information and apply it to multi-criteria group decision-making problems. The theory of intuitionistic 2-tuple fuzzy linguistic elements (I2FLEs) is useful for modeling impressions and quantifying the ambiguous nature of subjective judgments in a convenient manner. The family of ELECTRE methods is well known and widely used outranking method, but it has not been investigated within the intuitionistic 2-tuple fuzzy linguistic environment. ELECTRE uses the concept of an outranking relationship. Therefore, the directional Hausdorff distance, which uses I2FLEs, is proposed and the outranking relations are subsequently defined using this distance. Furthermore, using the proposed score and accuracy functions of I2FLEs, this paper also develops an outranking method based on intuitionistic fuzzy support function, intuitionistic fuzzy risk function, intuitionistic fuzzy credibility function, and the net outranking flow index similar to the PROMETHEE method. An illustrative example is given to demonstrate the practicality and effectiveness of the developed approaches. Finally, a comparative discussion of two decision-making methods is conducted to demonstrate the advantages of the proposed method over the other.

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

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Ashtiani B, Haghighirad F, Makui A, Montazer G (2009) Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets. Appl Soft Comput 9:457–461

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Beg I, Rashid T (2014) Hesitant intuitionistic fuzzy linguistic term set. Notes Intuit Fuzzy Sets 20(3):53–64

    MATH  Google Scholar 

  • Beg I, Rashid T (2016) An intuitionistic 2-tuple fuzzy linguistic information model and aggregation operators. Int J Intell Syst 31:569–592

    Article  Google Scholar 

  • Benayoun R, Roy B, Sussman B (1966) ELECTRE: Une méthode pour guider le choix en présence de points de vue multiples, Note de Travail 49. SEMA-METRA International, Direction Scientifique

  • Brans JP, Vincke PH (1985) The PROMETHEE method for multiple criteria decision making. Manag Sci 31(6):647–656

    Article  MATH  Google Scholar 

  • Chen TY, Tsao CY (2008) The interval-valued fuzzy TOPSIS method and experimental analysis. Fuzzy Sets Syst 159:1410–1428

    Article  MathSciNet  MATH  Google Scholar 

  • Chen N, Xu Z (2015) Hesitant fuzzy ELECTRE II approach: a new way to handle multi-criteria decision making problems. Inf Sci 292:175–197

    Article  Google Scholar 

  • de Almeida AT (2007) Multicriteria decision model for outsourcing contracts selection based on utility function and ELECTRE method. Comput Oper Res 34:3569–3574

    Article  MATH  Google Scholar 

  • Delgado M, Verdegay JL, Vila MA (1993) On aggregation operations of linguistic labels. Int J Intell Syst 8:351–370

    Article  MATH  Google Scholar 

  • Dong Y, Li CC, Herrera F (2016) Connecting the linguistic hierarchy and the numerical scale for the 2-tuple linguistic model and its uses to deal with hesitant unbalanced linguistic information. Inf Sci 367–368:259–278

    Article  Google Scholar 

  • Faizi S, Rashid T, Zafar S (2017) An outranking method for multi-criteria group decision making using hesitant intuitionistic fuzzy linguistic term sets. J Intell Fuzzy Syst 32(3):2153–2164

    Article  MATH  Google Scholar 

  • Figueira J, Mousseau V, Roy B (2005) ELECTRE methods. In: Fuguera J, Greco S, Ehrgott M (eds) Multiple criteria decision analysis: state of the art surveys, vol 39. Springer, Boston, pp 133–153

    Chapter  Google Scholar 

  • Herrera F, Herrera-Viedma E (2000a) Linguistic decision analysis: steps for solving decision problems under linguistic information. Fuzzy Sets Syst 115(1):67–82

    Article  MathSciNet  MATH  Google Scholar 

  • Herrera F, Martinez L (2000b) An approach for combining linguistic and numerical information based on the 2-tuple fuzzy linguistic representation model in decision making. Int J Uncertain Fuzziness Knowl Based Syst 8(5):539–562

    Article  MathSciNet  MATH  Google Scholar 

  • Herrera F, Martínez L (2000c) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8(6):746–752

    Article  Google Scholar 

  • Herrera F, Martinez L (2001) A model based on linguistic 2-tuple for dealing with multi-granular hierarchical linguistic contexts in multi-expert decision making. IEEE Trans Syst Man Cybern 31:227–234

    Article  Google Scholar 

  • Herrera F, Herrera-Viedma E, Verdegay JL (1996) A model of consensus in group decision making under linguistic assessments. Fuzzy Sets Syst 78(1):73–87

    Article  MathSciNet  MATH  Google Scholar 

  • Herrera F, Herrera-Viedma E, Martinez L (2000) A fusion approach for managing multi-granularity linguistic term sets in decision making. Fuzzy Sets Syst 114:43–58

    Article  MATH  Google Scholar 

  • Hwang CL, Yoon K (1981) Multiple attribute decision making. Springer, Berlin, pp 115–140

    Book  Google Scholar 

  • Li DF, Wang YC, Liu S, Shan F (2008) Fractional programming methodology for multi-attribute group decision making using IFS. Appl Soft Comput 8(1):219–225

    Article  Google Scholar 

  • Liao H, Xu Z (2015) Approaches to manage hesitant fuzzy linguistic information based on the cosine distance and similarity measures for HFLTSs and their application in qualitative decision making. Expert Syst Appl 42:5328–5336

    Article  Google Scholar 

  • Liao H, Xu Z, Zeng XJ (2014) Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making. Inf Sci 271:125–142

    Article  MathSciNet  MATH  Google Scholar 

  • Liao H, Xu Z, Zeng XJ (2015) Hesitant fuzzy linguistic VIKOR method and its application in qualitative multiple criteria decision making. IEEE Trans Fuzzy Syst 23(5):1343–1355

    Article  Google Scholar 

  • Liu XY, Ju YB, Yang SH (2014) Hesitant intuitionistic fuzzy linguistic aggregation operators and their applications to multiple attribute decision making. J Intell Fuzzy Syst 27(3):1187–1201

    MathSciNet  MATH  Google Scholar 

  • Peng HG, Wang JQ (2016) Hesitant uncertain linguistic Z-numbers and their application in multi-criteria group decision making problems. Int J Fuzzy Syst. https://doi.org/10.1007/s40815-016-0257-y

    Google Scholar 

  • Peng JJ, Wang JQ, Wang J, Yang LJ, Chen XH (2015) An extension of ELECTRE to multi-criteria decision making problems with multi-hesitant fuzzy sets. Inf Sci 307:113–126

    Article  MathSciNet  MATH  Google Scholar 

  • Peng JJ, Wang JQ, Wu X (2016) An extension of the ELECTRE approach with multi-valued neutrosophic information. Neural Comput Appl. https://doi.org/10.1007/s00521-016-2411-8

    Google Scholar 

  • Rashid T, Faizi S, Xu Z, Zafar S (2018) ELECTRE based outranking method for multi-criteria decision making using hesitant intuitionistic fuzzy linguistic term sets. Int J Fuzzy Syst. https://doi.org/10.1007/s40815-017-0297-y

    MathSciNet  MATH  Google Scholar 

  • Rodríguez RM, Martínez L, Herrera F (2011) Hesitant fuzzy linguistic term sets. In: Wang Y, Li T (eds) Foundations of Intelligent Systems. Advances in Intelligent and Soft Computing, vol 122. Springer, Berlin, Heidelberg

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Roy B, Vanderpooten D (1997) An overview on “The European school of MCDA: Emergence, basic features and current works”. Eur J Oper Res 99:26–27

    Article  MATH  Google Scholar 

  • Shen F, Xu J, Xu Z (2016) An outranking sorting method for multi-criteria group decision making using intuitionistic fuzzy sets. Inf Sci 334–335:338–353

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Vahdani B, Jabbari A, Roshanaei V, Zandieh M (2010) Extension of the ELECTRE method for decision making problems with interval weights and data. Int J Adv Manuf Technol 50(5–8):793–800

    Article  Google Scholar 

  • Wang JH, Hao JY (2006) A new version of 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 14(3):435–445

    Article  Google Scholar 

  • Wang JQ, Wang DD, Zhang HY, Chen XH (2014) Multi-criteria outranking approach with hesitant fuzzy sets. OR Spectr 36:1001–1019

    Article  MathSciNet  MATH  Google Scholar 

  • Wang J, Wang JQ, Zhang HY, Chen XH (2015) Multi-criteria decision making based on hesitant fuzzy linguistic term sets: an outranking approach. Knowl Based Syst 86:224–236

    Article  Google Scholar 

  • Wang JQ, Kuang JJ, Wang J, Zhang HY (2016) An extended outranking approach to rough stochastic multi-criteria decision making problems. Cognit Comput 8(6):1144–1160

    Article  Google Scholar 

  • Wei GW (2010) Extension of TOPSIS method for 2-tuple linguistic multiple attribute group decision making with incomplete weight information. Knowl Inf Syst 25:623–634

    Article  Google Scholar 

  • Wei CP, Zhao N, Tang XJ (2014) Operators and comparisons of hesitant fuzzy linguistic term sets. IEEE Trans Fuzzy Syst 22(3):575–585

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Zhou W, Xu Z (2016) Generalized asymmetric linguistic term set and its application to qualitative decision making involving risk appetites. Eur J Oper Res 254(2):610–621

    Article  MathSciNet  MATH  Google Scholar 

  • Zhou W, Xu Z, Chen M (2015) Preference relations based on hesitant-intuitionistic fuzzy information and their application in group decision making. Comput Ind Eng 87:163–175

    Article  Google Scholar 

  • Zhou H, Wang J, Zhang H (2016a) Stochastic multi-criteria decision making approach based on SMAA-ELECTRE with extended grey numbers. Int Trans Oper Res. https://doi.org/10.1111/itor.12380

    Google Scholar 

  • Zhou H, Wang J, Li X, Wang JQ (2016b) Intuitionistic hesitant linguistic sets and their application in multi-criteria decision making problems. Int J Oper Res 16:131–160

    Article  Google Scholar 

  • Zhou H, Wang JQ, Zhang HY (2018) Multi-criteria decision making approaches based on distance measures for linguistic hesitant fuzzy sets. J Oper Res Soc. https://doi.org/10.1057/jors.2016.41

    Google Scholar 

Download references

Acknowledgements

The authors would like to thank the editors and the anonymous reviewers, whose insightful comments and constructive suggestions helped us to significantly improve the quality of this paper.

Author information

Authors and Affiliations

  1. University of Management and Technology, Lahore, 54770, Pakistan

    Tabasam Rashid, Shahzad Faizi & Sohail Zafar

Authors
  1. Tabasam Rashid
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shahzad Faizi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sohail Zafar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tabasam Rashid.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Human and animal participants

This article does not contain any studies with human participants or animals performed by the author.

Consent

It is submitted with the consent of all the authors.

Additional information

Communicated by V. Loia.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rashid, T., Faizi, S. & Zafar, S. Outranking method for intuitionistic 2-tuple fuzzy linguistic information model in group decision making. Soft Comput 23, 6145–6155 (2019). https://doi.org/10.1007/s00500-018-3268-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-018-3268-9

Keywords

Search

Navigation