A new last aggregation method of multi-attributes group decision making based on concepts of TODIM, WASPAS and TOPSIS under interval-valued intuitionistic fuzzy uncertainty


Due to the complexity of decision making under uncertainty and the existence of various and often conflicting criteria, several methods have been proposed to facilitate decision making, and fuzzy logic has been used successfully to address this issue. This paper presents a new framework for solving multi-attributes group decision-making problems under fuzzy environments. The proposed algorithm has several features. First of all, the TODIM (an acronym in Portuguese for interactive multi-criteria decision making) method under interval-valued intuitionistic fuzzy uncertainty is employed. Moreover, objective and subjective weights for each decision maker are used to address this last aggregation approach. To consider weights of attributes, knowledge measure in addition to a new mathematical approach is introduced. A new aggregation and ranking method based on the WASPAS and TOPSIS methods, namely WT method, is presented and applied in this paper. Finally, the effectiveness of the proposed framework is shown by comparing the results with two different real-world applications in the literature.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3


  1. 1.

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

    MathSciNet  MATH  Google Scholar 

  2. 2.

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

    MATH  Google Scholar 

  3. 3.

    Banaeian N, Mobli H, Fahimnia B, Nielsen IE, Omid M (2018) Green supplier selection using fuzzy group decision making methods: a case study from the agri-food industry. Comput Oper Res 89:337–347

    MathSciNet  MATH  Google Scholar 

  4. 4.

    Baykasoğlu A, Gölcük İ (2017) Development of an interval type-2 fuzzy sets based hierarchical MADM model by combining DEMATEL and TOPSIS. Expert Syst Appl 70:37–51

    Google Scholar 

  5. 5.

    Beliakov G, Pradera A, Calvo T (2007) Aggregation functions: a guide for practitioners, vol 221. Springer, Heidelberg

    MATH  Google Scholar 

  6. 6.

    Büyüközkan G, Göçer F (2017) Application of a new combined intuitionistic fuzzy MCDM approach based on axiomatic design methodology for the supplier selection problem. Appl Soft Comput 52:1222–1238

    Google Scholar 

  7. 7.

    Büyüközkan G, Göçer F (2017) Smart medical device selection based on interval valued intuitionistic fuzzy VIKOR. In: Advances in fuzzy logic and technology 2017. Springer, Cham, pp 306–317

  8. 8.

    Büyüközkan G, Güleryüz S (2016) Multi criteria group decision making approach for smart phone selection using intuitionistic fuzzy TOPSIS. Int J Comput Intell Syst 9(4):709–725

    Google Scholar 

  9. 9.

    Chen TY (2015) IVIF-PROMETHEE outranking methods for multiple criteria decision analysis based on interval-valued intuitionistic fuzzy sets. Fuzzy Optim Decis Mak 14(2):173–198

    MathSciNet  MATH  Google Scholar 

  10. 10.

    Das S, Dutta B, Guha D (2016) Weight computation of criteria in a decision-making problem by knowledge measure with intuitionistic fuzzy set and interval-valued intuitionistic fuzzy set. Soft Comput 20(9):3421–3442

    MATH  Google Scholar 

  11. 11.

    Garg H (2016) A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems. Appl Soft Comput 38:988–999

    Google Scholar 

  12. 12.

    Gitinavard H, Mousavi SM, Vahdani B (2017) Soft computing-based new interval-valued hesitant fuzzy multi-criteria group assessment method with last aggregation to industrial decision problems. Soft Comput 21(12):3247–3265

    MATH  Google Scholar 

  13. 13.

    Gomes LFAM (2009) An application of the TODIM method to the multicriteria rental evaluation of residential properties. Eur J Oper Res 193(1):204–211

    MATH  Google Scholar 

  14. 14.

    Gomes LFAM, Lima MMPP (1992) TODIM: basics and application to multicriteria ranking of projects with environmental impacts. Found Comput Decis Sci 16(4):113–127

    MATH  Google Scholar 

  15. 15.

    Hajighasemi Z, Mousavi SM (2018) A new approach in failure modes and effects analysis based on compromise solution by considering objective and subjective weights with interval-valued intuitionistic fuzzy sets. Iran J Fuzzy Syst 15(1):139–161

    MathSciNet  MATH  Google Scholar 

  16. 16.

    Hashemi H, Bazargan J, Mousavi SM (2013) A compromise ratio method with an application to water resources management: an intuitionistic fuzzy set. Water Resour Manag 27:2029–2051

    Google Scholar 

  17. 17.

    Hwang CL, Yoon K (1981) Multiple attribute decision making: a state of the art survey. In: Lecture notes in economics and mathematical systems, vol 186

  18. 18.

    Jato-Espino D, Castillo-Lopez E, Rodriguez-Hernandez J, Canteras-Jordana JC (2014) A review of application of multi-criteria decision making methods in construction. Autom Constr 45:151–162

    Google Scholar 

  19. 19.

    Keshavarz Ghorabaee M (2016) Developing an MCDM method for robot selection with interval type-2 fuzzy sets. Robot Comput Integr Manuf 37:221–232

    Google Scholar 

  20. 20.

    Keshavarz Ghorabaee M, Amiri M, Sadaghiani JS, Goodarzi GH (2014) Multiple criteria group decision-making for supplier selection based on COPRAS method with interval type-2 fuzzy sets. Int J Adv Manuf Technol 75(5–8):1115–1130

    Google Scholar 

  21. 21.

    Keshavarz Ghorabaee M, Zavadskas EK, Amiri M, Esmaeili A (2016) Multi-criteria evaluation of green suppliers using an extended WASPAS method with interval type-2 fuzzy sets. J Clean Prod 137:213–229

    Google Scholar 

  22. 22.

    Krohling RA, Pacheco AG (2014) Interval-valued intuitionistic fuzzy TODIM. Procedia Comput Sci 31:236–244

    Google Scholar 

  23. 23.

    Krohling RA, Pacheco AG, Siviero AL (2013) IF-TODIM: an intuitionistic fuzzy TODIM to multi-criteria decision making. Knowl Based Syst 53:142–146

    Google Scholar 

  24. 24.

    Li DF (2011) Extension principles for interval-valued intuitionistic fuzzy sets and algebraic operations. Fuzzy Optim Decis Mak 10(1):45–58

    MathSciNet  MATH  Google Scholar 

  25. 25.

    Liu HC, Ren ML, Wu J, Lin QL (2014) An interval 2-tuple linguistic MCDM method for robot evaluation and selection. Int J Prod Res 52(10):2867–2880

    Google Scholar 

  26. 26.

    Liu W, Li L (2015) An approach to determining the integrated weights of decision makers based on interval number group decision matrices. Knowl Based Syst 90:92–98

    Google Scholar 

  27. 27.

    Lourenzutti R, Krohling RA (2013) A study of TODIM in a intuitionistic fuzzy and random environment. Expert Syst Appl 40(16):6459–6468

    Google Scholar 

  28. 28.

    Mohagheghi V, Mousavi SM, Siadat A (2016) Best product end-of-life scenario selection by a new decision-making process under Atanassov fuzzy uncertainty. In: 2016 IEEE international conference on management of innovation and technology (ICMIT), pp 313–317

  29. 29.

    Mohagheghi V, Mousavi SM, Aghamohagheghi M, Vahdani B (2017) A new approach of multi-criteria analysis for the evaluation and selection of sustainable transport investment projects under uncertainty: a case study. Int J Comput Intell Syst 10(1):605–626

    Google Scholar 

  30. 30.

    Mohagheghi V, Mousavi SM, Vahdani B, Shahriari MR (2017) R&D project evaluation and project portfolio selection by a new interval type-2 fuzzy optimization approach. Neural Comput Appl 28(12):3869–3888

    Google Scholar 

  31. 31.

    Mousavi SM, Vahdani B, Sadigh Behzadi S (2016) Designing a model of intuitionistic fuzzy VIKOR in multi-attribute group decision-making problems. Iran J Fuzzy Syst 13(1):45–65

    MathSciNet  Google Scholar 

  32. 32.

    Mousavi SM, Vahdani B (2016) Cross-docking location selection in distribution systems: a new intuitionistic fuzzy hierarchical decision model. Int J Comput Intell Syst 9(1):91–109

    Google Scholar 

  33. 33.

    Mousavi-Nasab SH, Sotoudeh-Anvari A (2017) A comprehensive MCDM-based approach using TOPSIS, COPRAS and DEA as an auxiliary tool for material selection problems. Mater Des 121:237–253

    Google Scholar 

  34. 34.

    Nassereddine M, Eskandari H (2017) An integrated MCDM approach to evaluate public transportation systems in Tehran. Transp Res Part A Policy Pract 106:427–439

    Google Scholar 

  35. 35.

    Nayagam VLG, Jeevaraj S, Dhanasekaran P (2017) An intuitionistic fuzzy multi-criteria decision-making method based on non-hesitance score for interval-valued intuitionistic fuzzy sets. Soft Comput 21(23):7077–7082

    MATH  Google Scholar 

  36. 36.

    Onat NC, Gumus S, Kucukvar M, Tatari O (2016) Application of the TOPSIS and intuitionistic fuzzy set approaches for ranking the life cycle sustainability performance of alternative vehicle technologies. Sustain Prod Consum 6:12–25

    Google Scholar 

  37. 37.

    Otay İ, Oztaysi B, Onar SC, Kahraman C (2017) Multi-expert performance evaluation of healthcare institutions using an integrated intuitionistic fuzzy AHP&DEA methodology. Knowl Based Syst 133:90–106

    Google Scholar 

  38. 38.

    Pal NR, Bustince H, Pagola M, Mukherjee UK, Goswami DP, Beliakov G (2013) Uncertainties with Atanassov’s intuitionistic fuzzy sets: fuzziness and lack of knowledge. Inf Sci 228:61–74

    MathSciNet  MATH  Google Scholar 

  39. 39.

    Qin J, Liu X, Pedrycz W (2017) An extended TODIM multi-criteria group decision making method for green supplier selection in interval type-2 fuzzy environment. Eur J Oper Res 258(2):626–638

    MathSciNet  MATH  Google Scholar 

  40. 40.

    Qin Q, Liang F, Li L, Chen YW, Yu GF (2017) A TODIM-based multi-criteria group decision making with triangular intuitionistic fuzzy numbers. Appl Soft Comput 55:93–107

    Google Scholar 

  41. 41.

    Ren P, Xu Z, Liao H, Zeng XJ (2017) A thermodynamic method of intuitionistic fuzzy MCDM to assist the hierarchical medical system in China. Inf Sci 420:490–504

    Google Scholar 

  42. 42.

    Rostamzadeh R, Keshavarz Ghorabaee M, Govindan K, Esmaeili A, Nobar HBK (2018) Evaluation of sustainable supply chain risk management using an integrated fuzzy TOPSIS-CRITIC approach. J Clean Prod 175:651–669

    Google Scholar 

  43. 43.

    Sen DK, Datta S, Mahapatra SS (2015) Extension of TODIM combined with grey numbers: an integrated decision making module. Grey Syst Theory Appl 5(3):367–391

    Google Scholar 

  44. 44.

    Vahdani B, Mousavi SM, Tavakkoli-Moghaddam R, Ghodratnama A, Mohammadi M (2014) Robot selection by a multiple criteria complex proportional assessment method under an interval-valued fuzzy environment. Int J Adv Manuf Technol 73(5–8):687–697

    Google Scholar 

  45. 45.

    Vinodh S, Balagi TS, Patil A (2016) A hybrid MCDM approach for agile concept selection using fuzzy DEMATEL, fuzzy ANP and fuzzy TOPSIS. Int J Adv Manuf Technol 83(9–12):1979–1987

    Google Scholar 

  46. 46.

    Wang P, Zhu Z, Wang Y (2016) A novel hybrid MCDM model combining the SAW, TOPSIS and GRA methods based on experimental design. Inf Sci 345:27–45

    Google Scholar 

  47. 47.

    Wei C, Ren Z, Rodríguez RM (2015) A hesitant fuzzy linguistic TODIM method based on a score function. Int J Comput Intell Syst 8(4):701–712

    Google Scholar 

  48. 48.

    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

    Google Scholar 

  49. 49.

    Ye F (2010) An extended TOPSIS method with interval-valued intuitionistic fuzzy numbers for virtual enterprise partner selection. Expert Syst Appl 37(10):7050–7055

    Google Scholar 

  50. 50.

    Yu SM, Wang J, Wang JQ (2018) An extended TODIM approach with intuitionistic linguistic numbers. Int Trans Oper Res 25(3):781–805

    MathSciNet  MATH  Google Scholar 

  51. 51.

    Zavadskas EK, Antucheviciene J, Hajiagha SHR, Hashemi SS (2014) Extension of weighted aggregated sum product assessment with interval-valued intuitionistic fuzzy numbers (WASPAS-IVIF). Appl Soft Comput 24:1013–1021

    Google Scholar 

  52. 52.

    Zavadskas EK, Turskis Z, Antucheviciene J, Zakarevicius A (2012) Optimization of weighted aggregated sum product assessment/Svorinio agreguoto alternatyviu sprendimu vertinimo optimizavimas. Elektronika ir elektrotechnika 122(6):3–6

    Google Scholar 

  53. 53.

    Zhang X, Xu Z (2015) Soft computing based on maximizing consensus and fuzzy topsis approach to interval-valued intuitionistic fuzzy group decision making. Appl Soft Comput 26:42–56

    Google Scholar 

  54. 54.

    Zhao H, Xu Z, Yao Z (2016) Interval-valued intuitionistic fuzzy derivative and differential operations. Int J Comput Intell Syst 9(1):36–56

    Google Scholar 

Download references


The authors would like to thank anonymous referees for their valuable comments and recommendations on this paper.

Author information




The authors of this research confirm the change in authorship based on their contributions in the revised version.

Corresponding author

Correspondence to S. Meysam Mousavi.

Ethics declarations

Conflict of interest

Authors declare that they have no conflict of interest.

Informed consent

Informed consent was not required as no human or animals were involved.

Human and animal rights

This article does not contain any studies with human or animal subjects performed by any of the authors.

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

Verify currency and authenticity via CrossMark

Cite this article

Davoudabadi, R., Mousavi, S.M. & Mohagheghi, V. A new last aggregation method of multi-attributes group decision making based on concepts of TODIM, WASPAS and TOPSIS under interval-valued intuitionistic fuzzy uncertainty. Knowl Inf Syst 62, 1371–1391 (2020). https://doi.org/10.1007/s10115-019-01390-x

Download citation


  • Interval-valued intuitionistic fuzzy sets (IVIFSs)
  • Multi-attributes group decision-making (MAGDM) problems
  • Objective and subjective weights
  • Last aggregation