Skip to main content
SpringerLink
Log in

An improved TODIM method based on the hesitant fuzzy psychological distance measure

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

The distance measure plays an important role in the hesitant fuzzy theory. Experts always focus on the attributes aggregation of hesitant fuzzy information, ignoring the preference relationships between alternatives. Therefore, it is necessary to consider the competition effect between alternatives and develop a more suitable distance measure. Considering the background information of the connections and competitive relationships between different alternatives, the hesitant fuzzy psychological distance measure is proposed. Based on which, a novel similarity measure for hesitant fuzzy information is also developed. Next, an improved TODIM based on the hesitant fuzzy psychological distance measure is proposed for decision making problems. At last but not least, we apply the proposed improved TODIM to the application of the temporary rescue airport decision making problem of the Arctic Northwest Passage. The results demonstrate the advantages of the proposed method in decision making under the hesitant fuzzy environment.

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

  1. Thomas M, Tsai CI (2012) Psychological distance and subjective experience: How distancing reduces the feeling of difficulty. J Consum Res 39:324–340

    Article  Google Scholar 

  2. Torra V, Narukawa Y (2009) On hesitant fuzzy sets and decision. in: The 18th IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, pp. 1378–1382.

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

    MATH  Google Scholar 

  4. Krishankumar R, Subrajaa LS, Ravichandran KS et al (2019) A Framework for multi-attribute group decision-making using double hierarchy hesitant fuzzy linguistic term set. Int J Fuzzy Syst 21:1130–1143

    Article  MathSciNet  Google Scholar 

  5. Krishankumar R, Ravichandran KS, Shyam V et al (2020) Multi-attribute group decision-making using double hierarchy hesitant fuzzy linguistic preference information. Neural Comput Appl. https://doi.org/10.1007/s00521-020-04802-0

    Article  Google Scholar 

  6. Farhadinia B (2016) Hesitant fuzzy set lexicographical ordering and its application to multi-attribute decision making. Inf Sci 327:233–245

    Article  MathSciNet  Google Scholar 

  7. Krishankumar R, Ravichandran KS, Ahmed MI et al (2019) Interval-valued probabilistic hesitant fuzzy set based muirhead mean for multi-attribute group decision-making. Mathematics 7:342

    Article  Google Scholar 

  8. Krishankumar R, Ravichandran KS, Kar S et al (2019) Interval-valued probabilistic hesitant fuzzy set for multi-criteria group decision-making. Soft Comput 23:10853–10879

    Article  Google Scholar 

  9. Krishankumar R, Ravichandran KS, Premaladha J et al (2018) Framework under a linguistic hesitant fuzzy set for solving multi-criteria group decision making problems. Sustainability 10:2608

    Article  Google Scholar 

  10. Yang LZ, Zhang R, Hou TP, Hao ZN, Liu J (2016) Hesitant cloud model and its application in the risk assessment of “The Twenty-First Century Maritime Silk Road”. Math Probl Eng 6:1–11

    MathSciNet  Google Scholar 

  11. Zeng WY, Li DQ (2016) Distance and similarity measures between hesitant fuzzy sets and their application in pattern recognition. Pattern Recogn Lett 84:267–271

    Article  Google Scholar 

  12. Zhang F, Chen S, Li J et al (2016) New distance measures on hesitant fuzzy sets based on the cardinality theory and their application in pattern recognition. Soft Comput 22:1–9

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  15. Li D, Zeng W, Zhao Y (2015) Note on distance measure of hesitant fuzzy sets. Inf Sci 321:103–115

    Article  MathSciNet  Google Scholar 

  16. Xu ZS, Xia MM (2012) Hesitant fuzzy entropy and cross-entropy and their use in multi-attribute decision making. Int J Intell Syst 27:799–822

    Article  Google Scholar 

  17. Das S, Malakar D, Kar S et al (2019) Correlation measures of hesitant fuzzy soft sets and their application in decision making. Neural Comput Appl 31:1023–1039

    Article  Google Scholar 

  18. Hong DH, Choi CH (2000) Multi-criteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst 114:103–113

    Article  Google Scholar 

  19. Huber J, Payne JW, Puto C (1982) Adding asymmetrically dominated alternatives-violations of regularity and the similarity hypothesis. J Consum Res 9:90–98

    Article  Google Scholar 

  20. Wedell DH (1991) Distinguishing among models of contextually induced preference reversals. J Exp Psychol Learn Mem Cogn 17:767–778

    Article  Google Scholar 

  21. Berkowitsch NAJ, Scheibehenne B, Rieskamp J, Matthaeus M (2015) A generalized distance function for preferential choices. Br J Math Stat Psychol 68:310–325

    Article  Google Scholar 

  22. Huang B, Li HX, Wei DK (2012) Dominance-based rough set model in intuitionistic fuzzy information systems. Knowl-Based Syst 28:115–123

    Article  Google Scholar 

  23. Huang B, Wei DK, Li HX et al (2013) Using a rough set model to extract rules in dominance-based interval-valued intuitionistic fuzzy information systems. Inf Sci 221:215–229

    Article  MathSciNet  Google Scholar 

  24. Wang JQ, Wang DD, Zhang DD et al (2014) Multi-criteria outranking approach with hesitant fuzzy sets. OR Spectrum 36:1001–1019

    Article  MathSciNet  Google Scholar 

  25. Farhadinia B, Herrera VE (2019) Sorting of decision-making methods based on their outcomes using dominance-vector hesitant fuzzy-based distance. Soft Comput 23:1109–1121

    Article  Google Scholar 

  26. Gomes LFAM, Lima MMPP (1991) TODIM: Basic and application to multi-criteria ranking of projects with environmental impacts. Fund Comput Decis Sci 16:113–127

    MATH  Google Scholar 

  27. Chen N, Xu ZS, Xia MM (2013) Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl Math Model 37:2197–2211

    Article  MathSciNet  Google Scholar 

  28. Nosofsky MR (1986) Attention, similarity and the identification-categorization relationship. J Exp Psychol: General 115:39–57

    Article  Google Scholar 

  29. Nosofsky RM, Zaki SR (2002) Exemplar and prototype models revisited: response strategies, selective attention and stimulus generalization. J Exp Psychol Learn Mem Cogn 28:924–940

    Article  Google Scholar 

  30. Hao ZN (2018) Several intuitionistic fuzzy multi-attribute decision making methods and their applications. Army Engineering University of PLA, Nanjing

    Google Scholar 

  31. Rooderkerk RP, Van Heerde HJ, Bijmolt THA (2011) Incorporating context effects into a choice model. J Market Res 48:767–780

    Article  Google Scholar 

  32. Li CQ, Zhao H, Xu ZS (2020) Hesitant fuzzy psychological distance measure. Int J Mach Learn Cybern. https://doi.org/10.1007/s13042-020-01102-w

    Article  Google Scholar 

  33. Liu F, Zhang WG (2013) TOPSIS-based consensus model for group decision-making with incomplete interval fuzzy preference relationships. IEEE Trans Cybern 44:1283–1294

    Article  Google Scholar 

  34. Chen TY (2013) An interval-valued intuitionistic fuzzy LINMAP method with inclusion comparison possibilities and hybrid averaging operations for multiple criteria group decision making. Knowl-Based Syst 45:134–146

    Article  Google Scholar 

  35. Chhipi-Shrestha CK, Hewage K, Sadiq R (2017) Selecting sustainability indicators for small to medium sized urban water systems using fuzzy ELECTRE. Water Environ Res 89:238–249

    Article  Google Scholar 

  36. Zhang XL, Xu ZS (2014) The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment. Knowl-Based Syst 61:48–58

    Article  Google Scholar 

  37. Erk R, Louie M Jr, Michael M et al (2011) Suspension freezing of bottom sediment and biota in the Northwest Passage and implications for Arctic Ocean sedimentation. Can J Earth Sci 29:693–703

    Google Scholar 

  38. Eicken H, Jones J, Meyer F et al (2011) Environmental security in Arctic ice-covered seas: from strategy to tactics of hazard identification and emergency response. Marine Technol Soc J 45:37–48

    Article  Google Scholar 

  39. 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 

Download references

Acknowledgements

The work was supported by the National Natural Science Foundation of China (No. 71571123, 71771155).

Author information

Authors and Affiliations

  1. Army Aviation Institute, Beijing, 101100, China

    Chenyang Song & Jian Hou

  2. Command and Control Engineering College, Army Engineering University of PLA, Nanjing, 211101, China

    Chenyang Song

  3. Business School, Sichuan University, Chengdu, 610064, China

    Zeshui Xu

Authors
  1. Chenyang Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zeshui Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jian Hou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zeshui Xu.

Additional information

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

Song, C., Xu, Z. & Hou, J. An improved TODIM method based on the hesitant fuzzy psychological distance measure. Int. J. Mach. Learn. & Cyber. 12, 973–985 (2021). https://doi.org/10.1007/s13042-020-01215-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-020-01215-2

Keywords

Search

Navigation