Skip to main content
SpringerLink
Log in

Complex interval-valued intuitionistic fuzzy TODIM approach and its application to group decision making

  • Original Research
  • Published:
Journal of Ambient Intelligence and Humanized Computing Aims and scope Submit manuscript

Abstract

Present work proposes novel fuzzy information based TODIM approaches that can deal with the evaluations under complex interval-valued intuitionistic fuzzy (CIVIF) environment. The proposed approaches have been referred to as complex interval-valued intuitionistic fuzzy-TODIM (CIVIF-TODIM) approaches. The proposed method encompasses the characteristic features of a complex intuitionistic fuzzy set, interval-valued fuzzy set, and TODIM methodology. At first, the definitions associated with CIVIF have been discussed and then the methodological steps involved in classical TODIM have been delineated. The classical TODIM approach is then extended to deal with group decision-making problems under the CIVIF environment. Robustness, effectiveness, applicability, and the improvements made to the extant fuzzy TODIM methods by the proposed methodology have been adjudged through the consideration of illustrative examples solved by the past researcher. Sensitivity analysis with respect to the attenuation factor as well as the criteria weights has been provided to justify the robustness of the proposed methods. A comparative analysis with the existing fuzzy-TODIM approaches has been delineated and a comprehensive analysis of the ranking results obtained for different distance measures at each value of attenuation factor is provided towards the end of the work. The carried out inclusive analysis on the approaches that have been proposed in the present work reveals that the proposed CIVIF fuzzy TODIM approaches are superior to the existing fuzzy TODIM methods. Therefore, the present study provides its contribution to the domain of decision-making framework through the approaches that provide for dealing with complex, uncertain, and linguistic information in an efficient manner.

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
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Alkouri AMDJS, Salleh AR (2012) Complex intuitionistic fuzzy sets. In: AIP conference proceedings, American institute of physics, international conference on fundamental and applied sciences (ICFAS 2012) conference 12th to 14th June 2012, vol 1482, no 1. Kuala Lumpur, Malaysia, pp 464–470

    Google Scholar 

  • Alkouri AUM, Salleh AR (2013) Complex Atanassov's intuitionistic fuzzy relation. Abstr Appl Anal 2013:1–18

    MathSciNet  MATH  Google Scholar 

  • Arora R, Garg H (2018) A robust correlation coefficient measure of dual hesitant fuzzy soft sets and their application in decision making. Eng Appl Artif Intell 72:80–92

    Google Scholar 

  • Atanassov KT (1986) Intuitionistic fuzzy sets. Intuitionistic fuzzy sets. Physica, Heidelberg, pp 1–137

    MATH  Google Scholar 

  • Atanassov KT (1989) More on intuitionistic fuzzy sets. Fuzzy Sets Syst 33(1):37–45

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Cao YX, Zhou H, Wang JQ (2018) An approach to interval-valued intuitionistic stochastic multi-criteria decision-making using set pair analysis. Int J Mach Learn Cybern 9(4):629–640

    Google Scholar 

  • Chen CT (2000) Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets Syst 114(1):1–9

    MATH  Google Scholar 

  • Chen SM, Chang CH (2015) A novel similarity measure between Atanassov’s intuitionistic fuzzy sets based on transformation techniques with applications to pattern recognition. Inf Sci 291:96–114

    Google Scholar 

  • Chen SM, Tsai WH (2016) Multiple attribute decision making based on novel interval-valued intuitionistic fuzzy geometric averaging operators. Inf Sci 367–368:1045–1065

    MATH  Google Scholar 

  • Dai S, Bi L, Hu B (2019) Distance measures between the interval-valued complex fuzzy sets. Mathematics 7(6):549

    Google Scholar 

  • 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 

  • Fan ZP, Zhang X, Chen FD, Liu Y (2013) Extended TODIM method for hybrid multiple attribute decision making problems. Knowl-Based Syst 1(42):40–48

    Google Scholar 

  • Garg H (2016a) Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm and their application to decision making. Comput Ind Eng 101:53–69

    Google Scholar 

  • Garg H (2016b) 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 

  • Garg H (2017) Novel intuitionistic fuzzy decision making method based on an improved operation laws and its application. Eng Appl Artif Intell 60:164–174

    Google Scholar 

  • Garg H (2018a) Some arithmetic operations on the generalized sigmoidal fuzzy numbers and its application. Granular Comput 3(1):9–25

    Google Scholar 

  • Garg H (2018b) Arithmetic operations on generalized parabolic fuzzy numbers and its application. Proc Natl Acad Sci India Sect A 88(1):15–26

    MathSciNet  MATH  Google Scholar 

  • Garg H (2018c) Some robust improved geometric aggregation operators under interval-valued intuitionistic fuzzy environment for multi-criteria decision-making process. J Ind Manag Optim 14(1):283–308

    MathSciNet  MATH  Google Scholar 

  • Garg H, Arora R (2018a) Generalized and group-based generalized intuitionistic fuzzy soft sets with applications in decision-making. Appl Intell 48(2):343–356

    Google Scholar 

  • Garg H, Arora R (2018b) Novel scaled prioritized intuitionistic fuzzy soft interaction averaging aggregation operators and their application to multi criteria decision making. Eng Appl Artif Intell 71:100–112

    Google Scholar 

  • Garg H, Kumar K (2018) An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making. Soft Comput 22(15):4959–4970

    MATH  Google Scholar 

  • Garg H, Kumar K (2019) Improved possibility degree method for ranking intuitionistic fuzzy numbers and their application in multiattribute decision-making. Granular Comput 4(2):237–247

    Google Scholar 

  • Garg H, Rani D (2019) Complex interval-valued intuitionistic fuzzy sets and their aggregation operators. Fund Inform 164(1):61–101

    MathSciNet  MATH  Google Scholar 

  • Garg H, Singh S (2018) A novel triangular interval type-2 intuitionistic fuzzy sets and their aggregation operators. Iran J Fuzzy Syst 15(5):69–93

    MathSciNet  MATH  Google Scholar 

  • Geng Y, Liu P, Teng F, Liu Z (2017) Pythagorean fuzzy uncertain linguistic TODIM method and their application to multiple criteria group decision making. J Intell Fuzzy Syst 33(6):3383–3395

    Google Scholar 

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

    MATH  Google Scholar 

  • Hu J, Yang Y, Chen X (2018) A novel TODIM method-based three-way decision model for medical treatment selection. Int J Fuzzy Syst 20(4):1240–1255

    MathSciNet  Google Scholar 

  • Jiang Y, Liang X, Liang H (2017) An I-TODIM method for multi-attribute decision making with interval numbers. Soft Comput 21(18):5489–5506

    MATH  Google Scholar 

  • Jianqiang W, Zhong Z (2009) Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems. J Syst Eng Electron 20(2):321–326

    Google Scholar 

  • Kahneman D, Tversky A (1979) Prospect theory: an analysis of decision under risk. Econometrica 47(2):363–391

    MathSciNet  MATH  Google Scholar 

  • Kaur G, Garg H (2018) Multi-attribute decision-making based on bonferroni mean operators under cubic intuitionistic fuzzy set environment. Entropy 20(1):65

    MathSciNet  Google Scholar 

  • Kaur G, Garg H (2019) Generalized cubic intuitionistic fuzzy aggregation operators using t-norm operations and their applications to group decision-making process. Arab J Sci Eng 44(3):2775–2794

    Google Scholar 

  • Kumar T, Bajaj RK (2014) On complex intuitionistic fuzzy soft sets with distance measures and entropies. J Math 2014:1–12

    MathSciNet  Google Scholar 

  • Li Z, Gao H, Wei G (2018) Methods for multiple attribute group decision making based on intuitionistic fuzzy dombi hamy mean operators. Symmetry 10(11):574

    MATH  Google Scholar 

  • Lu J, Wei C (2019) TODIM method for performance appraisal on social-integration-based rural reconstruction with interval-valued intuitionistic fuzzy information. J Intell Fuzzy Syst 37(2):1731–1740

    Google Scholar 

  • Lu J, He T, Wei G, Wu J, Wei C (2020) Cumulative prospect theory: performance evaluation of government purchases of home-based elderly-care services using the pythagorean 2-tuple Linguistic TODIM method. Int J Environ Res Public Health 17(6):1939

    Google Scholar 

  • 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 

  • Moshkovich HM, Gomes LFAM, Mechitov AI (2011) An integrated multicriteria decision-making approach to reale state evaluation: case of the TODIM method. Pesquisa Oper 31(1):03–20

    Google Scholar 

  • Nan J, Wang T, An J (2016) Intuitionistic fuzzy distance based TOPSIS method and application to MADM. Int J Fuzzy Syst Appl (IJFSA) 5(1):43–56

    Google Scholar 

  • Nie RX, Wang JQ (2020) Prospect theory-based consistency recovery strategies with multiplicative probabilistic linguistic preference relations in managing group decision making. Arab J Sci Eng 45(3):2113–2130

    Google Scholar 

  • Passos AC, Teixeira MG, Garcia KC, Cardoso AM, Gomes LFAM (2014) Using the TODIM-FSE method as a decision-making support methodology for oil spill response. Comp Oper Res 42:40–48

    MathSciNet  MATH  Google Scholar 

  • Ramot D, Milo R, Friedman M, Kandel A (2002) Complex fuzzy sets. IEEE Trans Fuzzy Syst 10(2):171–186

    Google Scholar 

  • Rani D, Garg H (2018) Complex intuitionistic fuzzy power aggregation operators and their applications in multicriteria decision-making. Expert Syst 35(6):e12325

    Google Scholar 

  • Shen KW, Wang XK, Qiao D, Wang JQ (2019) Extended Z-MABAC method based on regret theory and directed distance for regional circular economy development program selection with Z-information. IEEE Trans Fuzzy Syst (Early Access Article)

  • Shu MH, Cheng CH, Chang JR (2006) Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly. Microelectron Reliab 46(12):2139–2148

    Google Scholar 

  • Singh S, Garg H (2017) Distance measures between type-2 intuitionistic fuzzy sets and their application to multicriteria decision-making process. Appl Intell 46(4):788–799

    Google Scholar 

  • Soni N, Christian RA, Jariwala N (2016) Pollution potential ranking of industries using classical TODIM method. J Environ Protect 7(11):1645–1656

    Google Scholar 

  • Tian ZP, Wang J, Wang JQ, Chen XH (2018) Multicriteria decision-making approach based on gray linguistic weighted Bonferroni mean operator. Int Trans Oper Res 25(5):1635–1658

    MathSciNet  MATH  Google Scholar 

  • Tian ZP, Nie RX, Wang JQ, Luo H, Li L (2020) A prospect theory-based QUALIFLEX for uncertain linguistic Z-number multi-criteria decision-making with unknown weight information. J Intell Fuzzy Syst 38(2):1775–1787

    Google Scholar 

  • Tversky A, Kahneman D (1992) Advances in prospect theory: cumulative representation of uncertainty. J Risk Uncert 5(4):297–323

    MATH  Google Scholar 

  • Wang W, Liu X (2013a) The multi-attribute decision making method based on interval-valued intuitionistic fuzzy Einstein hybrid weighted geometric operator. Comput Math Appl 66(10):1845–1856

    MathSciNet  MATH  Google Scholar 

  • Wang W, Liu X (2013b) Interval-valued intuitionistic fuzzy hybrid weighted averaging operator based on Einstein operation and its application to decision making. J Intell Fuzzy Syst 25(2):279–290

    MathSciNet  MATH  Google Scholar 

  • Wang J, Wang JQ, Zhang HY, Chen XH (2016) Multi-criteria group decision-making approach based on 2-tuple linguistic aggregation operators with multi-hesitant fuzzy linguistic information. Int J Fuzzy Syst 18(1):81–97

    MathSciNet  Google Scholar 

  • Wang L, Wang L, Feng C, Zhou A, Yu W, Zhang Y, Zhang X (2017) Influence of main-panel angle on the hydrodynamic performance of a single-slotted cambered otter-board. Aquacult Fish 2(5):234–240

    Google Scholar 

  • Wang J, Wei G, Lu M (2018) TODIM method for multiple attribute group decision making under 2-tuple linguistic neutrosophic environment. Symmetry 10(10):486

    Google Scholar 

  • Wang L, Zhang HY, Wang JQ, Wu GF (2020a) Picture fuzzy multi-criteria group decision-making method to hotel building energy efficiency retrofit project selection. RAIRO Oper Res 54(1):211–229

    MathSciNet  MATH  Google Scholar 

  • Wang L, Wang XK, Peng JJ, Wang JQ (2020b) The differences in hotel selection among various types of travellers: a comparative analysis with a useful bounded rationality behavioural decision support model. Tour Manag 76:103961

    Google Scholar 

  • Wei G (2010) Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making. Appl Soft Comput 10(2):423–431

    Google Scholar 

  • Wei G, Zhao X (2012) Some induced correlated aggregating operators with intuitionistic fuzzy information and their application to multiple attribute group decision making. Expert Syst Appl 39(2):2026–2034

    Google Scholar 

  • Wu J, Huang HB, Cao QW (2013) Research on AHP with interval-valued intuitionistic fuzzy sets and its application in multi-criteria decision making problems. Appl Math Model 37(24):9898–9906

    MathSciNet  MATH  Google Scholar 

  • Wu L, Wang J, Gao H (2019a) Models for competiveness evaluation of tourist destination with some interval-valued intuitionistic fuzzy Hamy mean operators. J Intell Fuzzy Syst 36(6):5693–5709

    Google Scholar 

  • Wu L, Gao H, Wei C (2019b) VIKOR method for financing risk assessment of rural tourism projects under interval-valued intuitionistic fuzzy environment. J Intell Fuzzy Syst 37(2):2001–2008

    Google Scholar 

  • Wu L, Wei G, Wu J, Wei C (2020) Some Interval-valued intuitionistic fuzzy dombi heronian mean operators and their application for evaluating the ecological value of forest ecological tourism demonstration areas. Int J Environ Res Public Health 17(3):829

    Google Scholar 

  • Xu Z (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15(6):1179–1187

    Google Scholar 

  • Xu Z, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35(4):417–433

    MathSciNet  MATH  Google Scholar 

  • Yager RR (1977) Multiple objective decision-making using fuzzy sets. Int J Man Mach Stud 9(4):375–382

    MATH  Google Scholar 

  • Ye J (2013) Multiple attribute group decision-making methods with unknown weights in intuitionistic fuzzy setting and interval-valued intuitionistic fuzzy setting. Int J Gen Syst 42(5):489–502

    MathSciNet  MATH  Google Scholar 

  • Yu X, Xu Z (2013) Prioritized intuitionistic fuzzy aggregation operators. Inform Fus 14(1):108–116

    Google Scholar 

  • Yu W, Zhang Z, Zhong Q, Sun L (2017) Extended TODIM for multi-criteria group decision making based on unbalanced hesitant fuzzy linguistic term sets. Comput Ind Eng 114:316–328

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Zhang SF, Liu SY (2011) A GRA-based intuitionistic fuzzy multi-criteria group decision making method for personnel selection. Expert Syst Appl 38(9):11401–11405

    Google Scholar 

  • Zhang G, Wang JQ, Wang TL (2019) Multi-criteria group decision-making method based on TODIM with probabilistic interval-valued hesitant fuzzy information. Expert Syst 36(4):e12424

    Google Scholar 

  • Zindani D, Maity SR, Bhowmik S, Chakraborty S (2017) A material selection approach using the TODIM (TOmada de Decisao Interativa Multicriterio) method and its analysis. Int J Mater Res 108(5):345–354

    Google Scholar 

  • Zindani D, Maity SR, Bhowmik S (2018) A decision-making approach for material selection of polymeric composite bumper beam. In: Kumar K, Davim JP (eds) Composites and advanced materials for industrial applications. IGI Global, USA, pp 112–128

    Google Scholar 

  • Zindani D, Maity SR, Bhowmik S (2020) Interval-valued intuitionistic fuzzy TODIM method based on Schweizer–Sklar power aggregation operators and their applications to group decision making. Soft Comput 1–43 (Early access article)

Download references

Acknowledgment

The authors would like to acknowledge the Machine element laboratory, NIT Silchar for giving the computational facilities to carry out the research work.

Funding

No funding was received to perform the present work.

Author information

Authors and Affiliations

  1. Dept. of Mechanical Engineering, National Institute of Technology Silchar, Silchar, 788010, Assam, India

    Divya Zindani, Saikat Ranjan Maity & Sumit Bhowmik

Authors
  1. Divya Zindani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Saikat Ranjan Maity
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sumit Bhowmik
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Saikat Ranjan Maity.

Ethics declarations

Conflict of interest

All the authors of the present work has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals 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

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zindani, D., Maity, S.R. & Bhowmik, S. Complex interval-valued intuitionistic fuzzy TODIM approach and its application to group decision making. J Ambient Intell Human Comput 12, 2079–2102 (2021). https://doi.org/10.1007/s12652-020-02308-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12652-020-02308-0

Keywords

Search

Navigation