Skip to main content

Multi-criteria decision-making using a complete ranking of generalized trapezoidal fuzzy numbers

Soft Computing volume 25, pages 9859–9871 (2021)Cite this article

Abstract

The decision-making under several uncertainties is a major concern to choose the best alternative among the several separate alternatives. This paper deals with the uncertainty of using a complete ranking classification of generalized trapezoidal fuzzy numbers (GTrFNs). In the view of that several measures such as mode, spread, midpoint the score, radius, left and right fuzziness score and linguistic expression are considered to compute the ranking order of GTrFN. Using the proposed complete ranking of GTrFN, this paper presents a method for solving fuzzy multi-criteria decision-making problems. The comparative analysis of existing methods with our proposed method is also described.

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

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price includes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

References

  • Abbasbandy S, Asady B (2006) Ranking of fuzzy numbers by sign distance. Inf Sci 176(16):2405–2416

    MathSciNet  MATH  Google Scholar 

  • Abbasbandy S, Hajjari T (2009) A new approach for ranking of trapezoidal fuzzy numbers. Comput Math Appl 57(3):413–419

    MathSciNet  MATH  Google Scholar 

  • Abbasbandy S, Zhang L, Xu X, Tao L (2013) Some similarity measures for triangular fuzzy number and their applications in multiple criteria group decision-making. J Appl Math 2013(1):538–561

    Google Scholar 

  • Alpay S, Iphar M (2018) Equipment selection based on two different fuzzy multi criteria decision making methods: fuzzy topsis and fuzzy vikor. Open Geosci 10(1):661–677

    Google Scholar 

  • Anand Raj P, Nagesh Kumar D (1999a) Ranking multi-criterion river basin planning alternatives using fuzzy numbers. Fuzzy Sets Syst 100(1):89–99

    Google Scholar 

  • Anand Raj P, Nagesh Kumar D (1999b) Ranking alternatives with fuzzy weights using maximizing set and minimizing set. Fuzzy Sets Syst 105(3):365–375

    MATH  Google Scholar 

  • Awasthi A, Chauhan S, Goyal S (2011) A multi-criteria decision making approach for location planning for urban distribution centers under uncertainty. Math Comput Model 53(1):98–109

    MathSciNet  MATH  Google Scholar 

  • Baas S, Kwakernaak H (1977) Rating and ranking of multiple-aspect alternatives using fuzzy sets. Automatica 13(1):47–58

    MathSciNet  MATH  Google Scholar 

  • Boender C, de Graan J, Lootsma F (1989) Multi-criteria decision analysis with fuzzy pairwise comparisons. Fuzzy Sets Syst 29(2):133–143

    MathSciNet  MATH  Google Scholar 

  • Chen S-H (1985) Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets Syst 17(2):113–129

    MathSciNet  MATH  Google Scholar 

  • Chen S-J, Chen S-M (2007) Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers. Appl Intell 26:1–11

    Google Scholar 

  • Chen S-M, Chen J-H (2009) Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads. Expert Syst Appl 36(3 Part 2):6833–6842

    Google Scholar 

  • Chen L-H, Lu H-W (2001) An approximate approach for ranking fuzzy numbers based on left and right dominance. Comput Math Appl 41(12):1589–1602

    MathSciNet  MATH  Google Scholar 

  • Chen S-M, Sanguansat K (2011) Analyzing fuzzy risk based on a new fuzzy ranking method between generalized fuzzy numbers. Expert Syst Appl 38:2163–2171

    Google Scholar 

  • Chen S-M, Munif A, Chen G-S, Liu H-C, Kuo B-C (2012) Fuzzy risk analysis based on ranking generalized fuzzy numbers with different left heights and right heights. Expert Systems Appl 39(7):6320–6334

    Google Scholar 

  • Chen X, Du H, Yang Y (2014) The interval-valued triangular fuzzy soft set and its method of dynamic decision making. J Appl Math. https://doi.org/10.1155/2014/132806

    MathSciNet  Article  MATH  Google Scholar 

  • Cheng C-H (1998) A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets Syst 95(3):307–317

    MathSciNet  MATH  Google Scholar 

  • Chu T-C, Tsao C-T (2002) Ranking fuzzy numbers with an area between the centroid point and original point. Comput Math Appl 43(1):111–117

    MathSciNet  MATH  Google Scholar 

  • Das S, Guha D (2016) A centroid-based ranking method of trapezoidal intuitionistic fuzzy numbers and its application to mcdm problems. Fuzzy Inf Eng 8(1):41–74

    MathSciNet  Google Scholar 

  • Deng Y, Zhenfu Z, Qi L (2006) Ranking fuzzy numbers with an area method using radius of gyration. Comput Math Appl 51(6):1127–1136

    MathSciNet  MATH  Google Scholar 

  • Fahmi A, Abdullah S, Amin F, Aslam M, Hussain S (2020) Trapezoidal linguistic cubic fuzzy topsis method and application in a group decision making program. J Intell Syst 29(1):1283–1300

    Google Scholar 

  • Fu S, Zhou H (2016) Triangular fuzzy number multi-attribute decision-making method based on set-pair analysis. J Softw Eng 11:116–122

    Google Scholar 

  • Jain R (1976) Decisionmaking in the presence of fuzzy variables. IEEE Trans Syst Man Cybern SMC–6(10):698–703

    MATH  Google Scholar 

  • Jiang W, Luo Y, Qin X-Y, Zhan J (2015) An improved method to rank generalized fuzzy numbers with different left heights and right heights. J Intell Fuzzy Syst 28:2343–2355

    MathSciNet  MATH  Google Scholar 

  • Kannan S (2008) Fuzzy model in decision making of alternatives. Int J Adv Fuzzy Sets Syst 3(3):1–19

    Google Scholar 

  • Kaya I, olak M, Terzi F (2019) A comprehensive review of fuzzy multi criteria decision making methodologies for energy policy making. Energy Strategy Rev 24:207–228

    Google Scholar 

  • Kumar A, Singh P, Kaur P, Kaur A (2010) Ranking of generalized trapezoidal fuzzy numbers based on rank, mode, divergence and spread. Turk J Fuzzy Syst 1(2):141–152

    Google Scholar 

  • Kumar A, Singh P, Kaur P, Kaur A (2011) A new approach for ranking of l-r type generalized fuzzy numbers. Expert Syst Appl 38(9):10906–10910

    MATH  Google Scholar 

  • Kumar A, Singh P, Kaur P, Kaur A (2011) Rm approach for ranking of lr type generalized fuzzy numbers. Soft Comput 15(7):1373–1381

    MATH  Google Scholar 

  • Lee-Kwang H, Lee Jee-Hyong (1999) A method for ranking fuzzy numbers and its application to decision-making. IEEE Trans Fuzzy Syst 7(6):677–685

    Google Scholar 

  • Li X, Chen X (2015) Multi-criteria group decision making based on trapezoidal intuitionistic fuzzy information. Appl Soft Comput J 30:454–461

    Google Scholar 

  • Liang C, Zhao S, Zhang J (2017) Multi-criteria group decision making method based on generalized intuitionistic trapezoidal fuzzy prioritized aggregation operators. Int J Mach Learn Cybern 8(2):597–610

    Google Scholar 

  • Liu P, Li Y, Antucheviien J (2016) Multi-criteria decision-making method based on intuitionistic trapezoidal fuzzy prioritised owa operator. Technol Econ Dev Econ 22(3):453–469

    Google Scholar 

  • Mahapatra GS, Roy T (2011) Optimal redundancy allocation in series-parallel system using generalized fuzzy number. Tamsui Oxford J Inf Math Sci 27:1–20

    MathSciNet  MATH  Google Scholar 

  • Mi W-J, Dai Y-W (2017) Risk mixed multi-criteria fuzzy group decision-making approach based on prospect theory. Kongzhi yu Juece Control Decis 32(7):1279–1285

    MATH  Google Scholar 

  • Nakamura K (1986) Preference relations on a set of fuzzy utilities as a basis for decision making. Fuzzy Sets Syst 20(2):147–162

    MathSciNet  MATH  Google Scholar 

  • Ponnialagan D, Selvaraj J, Velu LGN (2017) A complete ranking of trapezoidal fuzzy numbers and its applications to multi-criteria decision making. Neural Comput Appl 30:3303–3315

    Google Scholar 

  • Rezvani S (2013) A new method for ranking in areas of two generalized trapezoidal fuzzy numbers. Int J Fuzzy Logic Syst 3:17–24

    MathSciNet  Google Scholar 

  • Sha F, Zhongli L, Hangjun Z, Dan S, Yezhi X (2014) Trapezoidal fuzzy number attitude indicators group decision making approaches based on fuzzy language. J Appl Sci 14(19):2304–2308

    Google Scholar 

  • Shahsavari Pour N, Heydari A, Kazemi M, Karami M (2017) A novel method for ranking fuzzy numbers based on the different areas fuzzy number. Int J Math Oper Res 11:544–566

    MathSciNet  MATH  Google Scholar 

  • Shumaiza Akram M, Al-Kenani A, Alcantud J (2019) Group decision-making based on the vikor method with trapezoidal bipolar fuzzy information. Symmetry 11(1313):1–21

    Google Scholar 

  • Simo UF, Gwet H (2018) A new algorithm for ranking of trapezoidal fuzzy numbers. Int J Fuzzy Syst 20(8):2355–2367

    MathSciNet  Google Scholar 

  • Sivaraman G, Vishnukumar P, Raj M (2020) MCDM based on new membership and non-membership accuracy functions on trapezoidal-valued intuitionistic fuzzy numbers. Soft Comput 24(6):4283–4293

    MATH  Google Scholar 

  • Wang Y (2020) Combining quality function deployment with simple additive weighting for interval-valued fuzzy multi-criteria decision-making with dependent evaluation criteria. Soft Comput 24(10):7757–7767

    Google Scholar 

  • Wang X, Kerre EE (2001) Reasonable properties for the ordering of fuzzy quantities. Fuzzy Sets Syst 118(3):375–385

    MathSciNet  MATH  Google Scholar 

  • Wang J, Chen Q-H, Zhang H-Y, Chen X-H, Wang J-Q (2017) Multi-criteria decision-making method based on type-2 fuzzy sets. Filomat 31(2):431–450

    MathSciNet  Google Scholar 

  • Xing Wang Z, Ni Mo Y (2010) Ranking fuzzy numbers based on ideal solution. Fuzzy Inf Eng 2(1):27–36

    MATH  Google Scholar 

  • Xu P, Su X, Wu J, Sun X, Zhang Y, Deng Y (2012) A note on ranking generalized fuzzy numbers. Expert Syst Appl 39:6454–6457

    Google Scholar 

  • Yager RR (1981) A procedure for ordering fuzzy subsets of the unit interval. Inf Sci 24(2):143–161

    MathSciNet  MATH  Google Scholar 

  • Yi P, Wang L, Li W (2019) Density-clusters ordered weighted averaging operator based on generalized trapezoidal fuzzy numbers. Int J Intell Syst 34(11):2970–2987

    Google Scholar 

  • Yu VF, Chi HTX, Dat LQ, Phuc PNK, Wen Shen C (2013) Ranking generalized fuzzy numbers in fuzzy decision making based on the left and right transfer coefficients and areas. Appl Math Model 37(16):8106–8117

    MathSciNet  MATH  Google Scholar 

  • Zadeh L (1965) Fuzzy sets. Inf Control 8(3):338–353

    MATH  Google Scholar 

  • Zhang F, Ignatius J, Lim CP, Zhao Y (2014) A new method for ranking fuzzy numbers and its application to group decision making. Appl Math Model 38(4):1563–1582

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

We are grateful to editors and anonymous referees for their valuable comments and helpful suggestions, which have helped us to improve this work significantly.

Author information

Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Puducherry, Karaikal, 609609, India

    Dharmalingam Marimuthu & G. S. Mahapatra

Authors
  1. Dharmalingam Marimuthu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. S. Mahapatra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dharmalingam Marimuthu.

Ethics declarations

Conflict of interest

Authors declare no conflict of interests.

Ethical approval

This work is not assisted by any source or any organizations, and this article does not contain any analysis with human participants or animals performed by any of the authors.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Marimuthu, D., Mahapatra, G.S. Multi-criteria decision-making using a complete ranking of generalized trapezoidal fuzzy numbers. Soft Comput 25, 9859–9871 (2021). https://doi.org/10.1007/s00500-020-05322-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-020-05322-8

Keywords

  • Multi-criteria decision-making
  • Fuzzy number
  • Generalized trapezoidal fuzzy number
  • Ranking function
  • Midpoint score
  • Spread