Skip to main content
SpringerLink
Log in

A nonlinear programming approach to solve MADM problem with triangular fuzzy preference and non-preference information

  • Research Article
  • Published:
Optimization and Engineering Aims and scope Submit manuscript

Abstract

In this paper, we present a new approach to solve multi-attribute decision making (MADM) problems considering subjective preferences and non-preferences of the decision maker in the form of triangular fuzzy preference relations and triangular fuzzy non-preference relations, respectively. Some important characteristics of these relations are used to form non-linear programming problems corresponding to lower, middle, and upper limits of the triangular fuzzy numbers. The optimization problems corresponding to lower and upper limits are solved to obtain corresponding limits of basic triangular fuzzy multiplicative preference weights (TFMPWs) and basic triangular fuzzy multiplicative non-preference weights (TFMNPWs). The obtained optimal weight values are used to find the modal values of TFMPWs and TFMNPWs that helps in the ranking of the alternatives. The working of the proposed approach is demonstrated by solving a MADM problem from the literature. Furthermore, to validate the superiority of the proposed approach, a comparative analysis with similar existing approaches has been provided. The obtained results reveal the applicability and usefulness of the proposed approach.

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

Similar content being viewed by others

References

  • Atanassov KT (1999) Intuitionistic fuzzy sets. In: Intuitionistic fuzzy sets. Physica, Heidelberg, pp 1–137

  • Bridgman PW (1922) Dimensional analysis. Yale University Press, New Haven

    Google Scholar 

  • Chang PT, Lee ES (1995) The estimation of normalized fuzzy weights. Comput Math Appl 29(5):21–42

    Article  MathSciNet  Google Scholar 

  • Chen SJ, Hwang CL (1992) Fuzzy multiple attribute decision making: methods and applications. In: Lecture notes in economics and mathematical systems. Springer, Berlin, p 375

  • Chiclana F, Herrera-Viedma E, Alonso S, Herrera F (2009) Cardinal consistency of reciprocal preference relations: a characterization of multiplicative transitivity. IEEE Trans Fuzzy Syst 17(1):14–23

    Article  Google Scholar 

  • Deli I (2020) A TOPSIS method by using generalized trapezoidal hesitant fuzzy numbers and application to a robot selection problem. J Intell Fuzzy Syst 38(1):779–793

    Article  Google Scholar 

  • Deli I, Karaaslan F (2020) Bipolar FPSS-tsheory with applications in decision making. Afr Mat 31:493–505

    Article  MathSciNet  Google Scholar 

  • Deli I, Şubaş Y (2017) Some weighted geometric operators with SVTrN-numbers and their application to multi-criteria decision-making problems. J Intell Fuzzy Syst 32(1):291–301

    Article  Google Scholar 

  • Dubois DJ, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic Press, New York, p 144

    MATH  Google Scholar 

  • Fedrizzi M, Krej J (2015) A note on the paper fuzzy analytic hierarchy process: fallacy of the popular methods. Int J Uncertain Fuzz And Knowl Based Syst 23(06):965–970

    Article  MathSciNet  Google Scholar 

  • Gong ZW, Li LS, Zhou FX, Yao TX (2009) Goal programming approaches to obtain the priority vectors from the intuitionistic fuzzy preference relations. Comput Ind Eng 57(4):187–1193

    Article  Google Scholar 

  • Gong ZW, Li LS, Forrest J, Zhao Y (2011) The optimal priority models of the intuitionistic fuzzy preference relation and their application in selecting industries with higher meteorological sensitivity. Expert Syst Appl 38(4):4394–4402

    Article  Google Scholar 

  • Gupta P, Mehlawat MK, Grover N (2016) Intuitionistic fuzzy multi-attribute group decision-making with an application to plant location selection based on a new extended VIKOR method. Inf Sci 370:184–203

    Article  Google Scholar 

  • Gupta P, Mehlawat MK, Grover N, Pedrycz W (2018) Multi-attribute group decision making based on extended TOPSIS method under interval-valued intuitionistic fuzzy environment. Appl Soft Comput 69:554–567

    Article  Google Scholar 

  • Krej J (2017) On multiplicative consistency of interval and fuzzy reciprocal preference relations. Comput Ind Eng 111:67–78

    Article  Google Scholar 

  • Liu F, Zhang WG, Zhang LH (2014) Consistency analysis of triangular fuzzy reciprocal preference relations. Eur J Oper Res 235(3):718–726

    Article  MathSciNet  Google Scholar 

  • Liu F, Pedrycz W, Wang ZX, Zhang WG (2017) An axiomatic approach to approximation-consistency of triangular fuzzy reciprocal preference relations. Fuzzy Sets Syst 322:1–18

    Article  MathSciNet  Google Scholar 

  • Ma J, Fan ZP, Jiang YP, Mao JY, Ma L (2006) A method for repairing the inconsistency of fuzzy preference relations. Fuzzy Sets Syst 157(1):20–33

    Article  MathSciNet  Google Scholar 

  • Meng F, Chen X (2017) A new method for triangular fuzzy compare wise judgment matrix process based on consistency analysis. Int J Fuzzy Syst 19(1):27–46

    Article  MathSciNet  Google Scholar 

  • Nagoorgani A, Ponnalagu K (2012) A new approach on solving intuitionistic fuzzy linear programming problem. Appl Math Sci 6(70):3467–3474

    MathSciNet  MATH  Google Scholar 

  • Saaty TL (1977) A scaling method for priorities in hierarchical structures. J Math Psychol 15(3):234–281

    Article  MathSciNet  Google Scholar 

  • Saaty TL (1994) Fundamentals of decision making and priority theory with the AHP. RWS Publications, Pittsburgh

    Google Scholar 

  • Saaty TL (2008) Decision making with the analytic hierarchy process. Int J Serv Sci 1(1):83–98

    Google Scholar 

  • Tang J, Meng F (2017) A consistency-based method to decision making with triangular fuzzy multiplicative preference relations. Int J Fuzzy Syst 9(5):1317–1332

    Article  Google Scholar 

  • Uluçay V, Deli I, Ahin M (2018) Trapezoidal fuzzy multi-number and its application to multi-criteria decision-making problems. Neural Comput Appl 30(5):1469–1478

    Article  Google Scholar 

  • Wang ZJ (2015) Consistency analysis and priority derivation of triangular fuzzy preference relations based on modal value and geometric mean. Inf Sci 314:169–183

    Article  MathSciNet  Google Scholar 

  • Wang ZJ (2018) A goal programming based heuristic approach to deriving fuzzy weights in analytic form from triangular fuzzy preference relations. IEEE Trans Fuzzy Syst 27(2):234–248

    Article  Google Scholar 

  • Wang YM, Elhag TM (2006) On the normalization of interval and fuzzy weights. Fuzzy Sets Syst 157(18):2456–2471

    Article  MathSciNet  Google Scholar 

  • Xia M, Xu Z, Liao H (2013) Preference relations based on intuitionistic multiplicative information. IEEE Trans Fuzzy Syst 21(1):113–133

    Article  Google Scholar 

  • Xu Z (2013) Priority weight intervals derived from intuitionistic multiplicative preference relations. IEEE Trans Fuzzy Syst 21(4):642–654

    Article  Google Scholar 

  • Yoon K, Hwang CL (1981) Multiple attribute decision making methods and applications. Springer, Berlin

    MATH  Google Scholar 

  • Zhu B, Xu Z (2014) Consistency measures for hesitant fuzzy linguistic preference relations. IEEE Trans Fuzzy Syst 22(1):35–45

    Article  Google Scholar 

Download references

Acknowledgements

The authors are gratitude to Editor-in-Chief, Guest Editors, and all the reviewers for their valuable comments. Author Faizan Ahemad is supported by DST INSPIRE Fellowship (DST/INSPIRE Fellowship/IF180317). The first author acknowledges the support through MATRICS Scheme of DST-SERB, New Delhi, India.

Author information

Authors and Affiliations

  1. Department of Operational Research, University of Delhi, Delhi, 110007, India

    Mukesh Kumar Mehlawat, Pankaj Gupta & Faizan Ahemad

Authors
  1. Mukesh Kumar Mehlawat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pankaj Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Faizan Ahemad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pankaj Gupta.

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

Mehlawat, M.K., Gupta, P. & Ahemad, F. A nonlinear programming approach to solve MADM problem with triangular fuzzy preference and non-preference information. Optim Eng 22, 1091–1116 (2021). https://doi.org/10.1007/s11081-020-09524-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11081-020-09524-9

Keywords

Search

Navigation