Skip to main content
SpringerLink
Log in

Multi-criteria decision making based on ranking of neutrosophic trapezoidal fuzzy numbers

  • Original Paper
  • Published:
Granular Computing Aims and scope Submit manuscript

Abstract

In this ebb and flow time, the neutrosophic set is a significant theme to exhibit the uncertain data, as it shows up the presence of three disjunctive segments, and it gives a wide scope of utilization in particular fields for the analysts. Neutrosophic sets are the extension of intuitionistic fuzzy sets to concentrate on the dubious, reluctant, and equivocal figures of genuine scientific problems. Ranking of neutrosophic fuzzy numbers is a challenging task. Only a very few models have been proposed in the literature for the ranking of neutrosophic fuzzy numbers. In this paper, we have first ranked the neutrosophic trapezoidal fuzzy numbers using the Euclidean measure to frame the centroid concept. We have studied a few properties of the ranking function. The effectiveness of the proposed ranking method is shown by comparative examples. Finally, the created positioning system is utilized to make a decision in the purchase problem.

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

Similar content being viewed by others

References

  • Ali M, Son LH, Deli I, Tien ND (2017) Bipolar neutrosophic soft sets and applications in decision making. J Intell Fuzzy Syst 33(6):4077–4087

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Biswas P, Pramanik S, Giri BC (2014) Cosine similarity measure based multi-attribute decision-making with trapezoidal fuzzy neutrosophic numbers. Neutrosophic Sets Syst 8:46–56

    Google Scholar 

  • Biswas P, Pramanik S, Giri BC (2018a) Distance measure based MADM strategy with interval trapezoidal neutrosophic numbers. Neutrosophic Sets Syst 19:40–46

    Google Scholar 

  • Biswas P, Pramanik S, Giri BC (2018) Multi-attribute group decision making based on expected value of neutrosophic trapezoidal numbers. In: New trends in neutrosophic theory and applications. European Union II, Brussels, pp 103–124

  • Biswas P, Pramanik S, Giri BC (2018c) TOPSIS strategy for multiattribute decision making with trapezoidal neutrosophic numbers. Neutrosophic Sets Syst 20(1):29–39

    Google Scholar 

  • Broumi S, Ye J, Smarandache F (2015) An extended TOPSIS method for multiple attribute decision making based on interval neutrosophic uncertain linguistic variables. Neutrosophic Sets Syst 8:22–31

    Google Scholar 

  • Broumi S, Smarandache F, Talea M, Bakali A (2016a) An introduction to bipolar single valued neutrosophic graph theory. Appl Mech Mater 841:184–191

    Article  Google Scholar 

  • Broumi S, Smarandache F, Talea M, Bakali A (2016) Single valued neutrosophic graphs: degree, order and size. In: Proceedings of IEEE international conference on fuzzy systems (FUZZ-IEEE), Vancouver, pp 2444–2451

  • Chen SM, Chang CH (2016) Fuzzy multiattribute decision making based on transformation techniques of intuitionistic fuzzy values and intuitionistic fuzzy geometric averaging operators. Inf Sci. https://doi.org/10.1016/j.ins.2016.02.049

    Article  MATH  Google Scholar 

  • Chen SM, Chen SW (2015) Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups and the probabilities of trends of fuzzy logical relationships. IEEE Trans Cybern 45(3):391–403

    Article  Google Scholar 

  • Chen SM, Niou SJ (2011) Fuzzy multiple attributes group decision-making based on fuzzy preference relations. Expert Syst Appl 38(4):3865–3872

    Article  Google Scholar 

  • Chen SM, Wang NY (2010) Fuzzy forecasting based on fuzzy-trend logical relationship groups. IEEE Trans Syst Man Cybern B Cybern 40(5):1343–1358

    Article  Google Scholar 

  • Chen SM, Kai Ko Y, Chang YC, Pan JS (2009) Weighted fuzzy interpolative reasoning based on weighted increment transformation and weighted ratio transformation techniques. IEEE Trans Fuzzy Syst 17(6):1412–1427

    Article  Google Scholar 

  • Chen SM, Chu H, Sheu T (2012) TAIEX forecasting using fuzzy time series and automatically generated weights of multiple factors. IEEE Trans Syst Man Cybern Part A Syst Hum 42(6):1485–1495

    Article  Google Scholar 

  • Chen SM, Chen SH, Lan TC (2016) Multicriteria decision making based on the TOPSIS method and similarity measures between intuitionistic fuzzy values. Inf Sci 367–368:279–295

    Article  Google Scholar 

  • Chen T, He SS, Wang JQ, Li L, Luo H (2019) Novel operations for linguistic neutrosophic sets on the basis of Archimedean copulas and co-copulas and their application in multi-criteria decision making problems. J Intell Fuzzy Syst 37(2):2887–2912

    Article  Google Scholar 

  • Cuong BC, Kreinovich V (2013) Picture fuzzy sets: a new concept for computational intelligence problems. In: Proceedings of the third world congress on information and communication technologies, Vietnam, pp 1–6

  • Deli I, Ali M, Smarandache F (2015) Bipolar neutrosophic sets and their application based on multi-criteria decision making problems. In: Proceedings of international conference on advanced mechatronic systems, China, pp 249–254

  • Deli I, Broumi S, Smarandache F (2015) On neutrosophic refined sets and their applications in medical diagnosis. J New Theory 6:88–98

    Google Scholar 

  • Dey PP, Pramanik S, Gir BC (2016) TOPSIS for solving multi-attribute decision making problems under bi-polar neutrosophic environment. In: New trends in neutrosophic theory and applications, ch. 5. European Union, Brussels, pp 65–77

  • Fahim A, Amin F, Ullah H (2019) Multiple attribute group decision making based on weighted aggregation operators of triangular neutrosophic cubic fuzzy numbers. Granul Comput. https://doi.org/10.1007/s41066-019-00205-2

    Article  Google Scholar 

  • Fahim A, Aslam M, Riaz M (2019) New approach of triangular neutrosophic cubic linguistic hesitant fuzzy aggregation operators. Granul Comput. https://doi.org/10.1007/s41066-019-00205-2

    Article  Google Scholar 

  • Jana C, Karaaslan F (2020) Dice and Jaccard similarity measures based on expected intervals of trapezoidal neutrosophic fuzzy numbers and their applications in multicriteria decision making. In: Optimization theory based on neutrosophic and plithogenic sets, pp 261–287

  • Jana C, Pal M, Karaaslan F, Wang J (2018) Trapezoidal neutrosophic aggregation operators and its application in multiple attribute decision making process. In: Science Iranica, pp 1–23

  • Liu P, You X (2019) Bidirectional projection measure of linguistic neutrosophic numbers and their application to multi-criteria group decision making. Comput Ind Eng 128:447–457

    Article  Google Scholar 

  • Pramanik S, Mallick R (2019) TODIM strategy for multi-attribute group decision making in trapezoidal neutrosophic number environment. Complex Intell Syst 5(4):379–389

    Article  Google Scholar 

  • Pramanik S, Dalapati S, Alam S, Roy TK (2018) VIKOR based MAGDM strategy under bipolar neutrosophic set environment. Neutrosophic Sets Syst 19:57–69

    Google Scholar 

  • Pramanik S, Dey PP, Smarandache F (2018) Correlation coefficient measures of interval bipolar neutrosophic sets for solving multi-attribute decision making problems. Neutrosophic Sets Syst 19:70–79

    Google Scholar 

  • Smarandache RF (1999) A unifying field in logics. In: Neutrosophy. Neutrosophic probability, set and logic. American Research Press, Rehoboth, pp 7–8

  • Tan R, Zhang W, Chen S (2017) Some generalized single valued neutrosophic linguistic operators and their application to multiple attribute group decision making. J Syst Sci Inf 5(2):148–162

    Google Scholar 

  • Tan RP, Zhang WD, Broumi S (2019) Solving methods of the shortest path problem based on the trapezoidal fuzzy neutrosophic numbers. Control Decis 34(4):851–860

    Google Scholar 

  • Tian ZP, Wang J, Zhang HY, Chen XH, Wang JQ (2016) Simplified neutrosophic linguistic normalized weighted Bonferroni mean operator and its application to multi-criteria decision-making problems. Filomat 30(12):3339–3360

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Wang JQ, Li XE (2015) TODIM method with multi-valued neutrosophic sets. Control Decis 30:1139–1142

    Google Scholar 

  • Wang H, Smarandache F, Zhang YQ, Sunderraman R (2012) Single valued neutrosophic sets. Tech Sci Appl Math 10:10–14

    MATH  Google Scholar 

  • Wang J, Gao H, Wei GW (2019) Some 2-tuple linguistic neutrosophic number Muirhead mean operators and their applications to multiple attribute decision making. J Exp Theor Artif Intell 31(3):409–439

    Article  Google Scholar 

  • Yang W, Pang Y (2018) New multiple attribute decision making method based on DEMATEL and TOPSIS for multivalued interval neutrosophicsets. Symmetry 10(4):115

    Article  Google Scholar 

  • Ye JA (2014) Multicriteria decision-making method using aggregation operators for simplified neutrosophic sets. J Intell Fuzzy Syst 26(5):2459–2466

    Article  MathSciNet  Google Scholar 

  • Ye J (2015) Trapezoidal neutrosophic set and its application to multiple attribute decision-making. Neural Comput Appl 26(5):1157–1166

    Article  Google Scholar 

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

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Kongu Engineering College, Erode, Tamil Nadu, India

    M. Suresh, K. Arun Prakash & S. Vengataasalam

Authors
  1. M. Suresh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Arun Prakash
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Vengataasalam
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Suresh.

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

Suresh, M., Arun Prakash, K. & Vengataasalam, S. Multi-criteria decision making based on ranking of neutrosophic trapezoidal fuzzy numbers. Granul. Comput. 6, 943–952 (2021). https://doi.org/10.1007/s41066-020-00240-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41066-020-00240-4

Keywords

Search

Navigation