Multi-criteria decision-making based on generalized prioritized aggregation operators under simplified neutrosophic uncertain linguistic environment | International Journal of Machine Learning and Cybernetics Skip to main content
Springer Nature Link
Log in

Multi-criteria decision-making based on generalized prioritized aggregation operators under simplified neutrosophic uncertain linguistic environment

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

A simplified neutrosophic uncertain linguistic set that integrates quantitative and qualitative evaluation can serve as an extension of both an uncertain linguistic variable and a simplified neutrosophic set. It can describe the real preferences of decision-makers and reflect their uncertainty, incompleteness and inconsistency. This paper focuses on multi-criteria decision-making (MCDM) problems in which the criteria occupy different priority levels and the criteria values take the form of simplified neutrosophic uncertain linguistic elements. Having reviewed the relevant literatures, this paper develops some generalized simplified neutrosophic uncertain linguistic prioritized weighted aggregation operators and applies them to solve MCDM problems. Finally, an illustrative example is given, and two cases of comparison analysis are conducted with other representative methods to demonstrate the effectiveness and feasibility of the developed approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

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

    Article  MATH  Google Scholar 

  2. Mardani A, Jusoh A, Zavadskas EK (2015) Fuzzy multiple criteria decision-making techniques and applications—two decades review from 1994 to 2014. Expert Syst Appl 42(8):4126–4148

    Article  Google Scholar 

  3. Wang XZ, Xing HJ, Li Y, Hua Q, Dong CR, Pedrycz W (2015) A study on relationship between generalization abilities and fuzziness of base classifiers in ensemble learning. IEEE Trans Fuzzy Syst 23(5):1638–1654

    Article  Google Scholar 

  4. Wang XZ, Ashfaq RAR, Fu AM (2015) Fuzziness based sample categorization for classifier performance improvement. J Intell Fuzzy Syst 29(3):1185–1196

    Article  MathSciNet  Google Scholar 

  5. Wang XZ (2015) Uncertainty in learning from big data-editorial. J Intell Fuzzy Syst 28(5):2329–2330

    Article  Google Scholar 

  6. Ashfaq RAR, Wang XZ, Huang JZX, Abbas H, He YL (2016) Fuzziness based semi-supervised learning approach for intrusion detection system. Inf Sci. doi:10.1016/j.ins.2016.04.019

    Google Scholar 

  7. He YL, Wang XZ, Huang JZ (2016) Fuzzy nonlinear regression analysis using a random weight network. Inf Sci. doi:10.1016/j.ins.2016.01.037

    Google Scholar 

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

    Article  MATH  Google Scholar 

  9. Yue ZL (2014) TOPSIS-based group decision-making methodology in intuitionistic fuzzy setting. Inf Sci 277:141–153

    Article  MathSciNet  MATH  Google Scholar 

  10. Wang CH, Wang J (2015) A multi-criteria decision-making method based on triangular intuitionistic fuzzy preference information. Intell Autom Soft Comput. doi:10.1080/10798587.2015.1095418

    Google Scholar 

  11. Chen SM, Cheng SH, Chiou CH (2016) Fuzzy multiattribute group decision making based on intuitionistic fuzzy sets and evidential reasoning methodology. Inf Fusion 27:215–227

    Article  Google Scholar 

  12. Martínez L, Ruan D, Herrera F, Herrera-Viedma E, Wang PP (2009) Linguistic decision making: tools and applications. Inf Sci 179(14):2297–2298

    Article  Google Scholar 

  13. Liu PD, Wang YM (2014) Multiple attribute group decision making methods based on intuitionistic linguistic power generalized aggregation operators. Appl Soft Comput 17:90–104

    Article  Google Scholar 

  14. Tian ZP, Wang J, Wang JQ, Chen XH (2015) Multi-criteria decision-making approach based on gray linguistic weighted Bonferroni mean operator. Int Trans Oper Res. doi:10.1111/itor.12220

    Google Scholar 

  15. Zhou H, Wang JQ, Zhang HY, Chen XH (2016) Linguistic hesitant fuzzy multi-criteria decision-making method based on evidential reasoning. Int J Syst Sci 47(2):314–327

    Article  MathSciNet  MATH  Google Scholar 

  16. Tian ZP, Wang J, Wang JQ, Zhang HY (2016) A likelihood-based qualitative flexible approach with hesitant fuzzy linguistic information. Cogn Comput. doi:10.1007/s12559-016-9400-1

    Google Scholar 

  17. Chen TY, Chang CH, Lu JFR (2013) The extended QUALIFLEX method for multiple criteria decision analysis based on interval type-2 fuzzy sets and applications to medical decision making. Eur J Oper Res 226(3):615–625

    Article  MathSciNet  MATH  Google Scholar 

  18. 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

    Article  MathSciNet  Google Scholar 

  19. Rodríguez RM, Martínez L (2013) An analysis of symbolic linguistic computing models in decision making. Int J Gen Syst 42(1):121–136

    Article  MathSciNet  MATH  Google Scholar 

  20. Xu ZS (2006) Induced uncertain linguistic OWA operators applied to group decision making. Inf Fusion 7:231–238

    Article  Google Scholar 

  21. Xu ZS (2009) An interactive approach to multiple attribute group decision making with multigranular uncertain linguistic information. Group Decis Negot 18(2):119–145

    Article  Google Scholar 

  22. Liu PD (2013) Some geometric aggregation operators based on interval intuitionistic uncertain linguistic variables and their application to group decision making. Appl Math Model 37(4):2430–2444

    Article  MathSciNet  MATH  Google Scholar 

  23. Li QX, Zhao XF, Wei GW (2014) Model for software quality evaluation with hesitant fuzzy uncertain linguistic information. J Intell Fuzzy Syst 26(6):2639–2647

    MathSciNet  MATH  Google Scholar 

  24. Smarandache F (1999) A unifying field in logics. Neutrosophy: neutrosophic probability, set and logic. American Research Press, Rehoboth

    MATH  Google Scholar 

  25. Wang HB, Smarandache F, Zhang YQ, Sunderraman R (2010) Single valued neutrosophic sets. Multispace Multistruct 4:410–413

    MATH  Google Scholar 

  26. Wang HB, Smarandache F, Zhang YQ, Sunderraman R (2005) Interval neutrosophic sets and logic: theory and applications in computing. Hexis, Phoenix

    MATH  Google Scholar 

  27. Broumi S, Deli I, Smarandache F (2015) N-valued interval neutrosophic sets and their application in medical diagnosis. Crit Rev Center Math Uncertain Creighton Univ USA 10:46–69

    Google Scholar 

  28. Smarandache F (2013) N-valued refined neutrosophic logic and its applications in physics. Progr Phys 4:143–146

    Google Scholar 

  29. Broumi S, Smarandache F, Maji PK (2014) Intuitionistic neutrosphic soft set over rings. Math Stat 2(3):120–126

    Google Scholar 

  30. Deli I (2015) NPN-soft sets theory and applications. Ann Fuzzy Math Inf 10(6):847–862

    MathSciNet  MATH  Google Scholar 

  31. Deli I, Broumi S (2015) Neutrosophic soft matrices and NSM-decision making. J Intell Fuzzy Syst 28(5):2233–2241

    Article  MathSciNet  Google Scholar 

  32. Deli I (2015) NPN-soft sets theory and applications. Ann Fuzzy Math Inf 10(6):847–862

    MathSciNet  MATH  Google Scholar 

  33. Broumi S, Smarandache F (2015) Interval-valued neutrosophic soft rough set. Int J Comput Math. doi:10.1155/2015/232919

    MathSciNet  Google Scholar 

  34. Deli I (2015) Interval-valued neutrosophic soft sets and its decision making. Int J Mach Learn Cybern. doi:10.1007/s13042-015-0461-3

    Google Scholar 

  35. Broumi S, Talea M, Bakali A, Smarandache F (2016) Single valued neutrosophic graphs. J N Theory 10:86–101

    Google Scholar 

  36. Broumi S, Talea M, Bakali A, Smarandache F (2016) On bipolar single valued neutrosophic graphs. J N Theory 11:84–102

    Google Scholar 

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

    Article  Google Scholar 

  38. Broumi S, Talea M, Bakali A, Smarandache F (2016) Interval valued neutrosophic graphs. SISOM Conference

  39. Broumi S, Talea M, Smarandache F, Bakali A (2016) Single valued neutrosophic graphs: degree, order and size. FUZZ IEEE Conference, p 8

  40. Liu PD, Chu YC, Li YW, Chen YB (2014) Some generalized neutrosophic number Hamacher aggregation operators and their application to group decision making. Int J Fuzzy Syst 16(2):242–255

    Google Scholar 

  41. Şahin R, Liu PD (2015) Maximizing deviation method for neutrosophic multiple attribute decision making with incomplete weight information. Neural Comput Appl. doi:10.1007/s00521-015-1995-8

    Google Scholar 

  42. Peng JJ, Wang JQ, Wang J, Zhang HY, Chen XH (2016) Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems. Int J Syst Sci 47(10):2342–2358

    Article  MATH  Google Scholar 

  43. Broumi S, Smarandache F (2014) Correlation coefficient of interval neutrosophic set. Appl Mech Mater 436:511–517

    Article  Google Scholar 

  44. Zhang HY, Ji P, Wang JQ, Chen XH (2015) An improved weighted correlation coefficient based on integrated weight for interval neutrosophic sets and its application in multi-criteria decision-making problems. Int J Comput Intell Syst 8(6):1027–1043

    Article  Google Scholar 

  45. Şahin R, Liu PD (2016) Correlation coefficient of single-valued neutrosophic hesitant fuzzy sets and its applications in decision making. Neural Comput Appl. doi:10.1007/s00521-015-2163-x

    Google Scholar 

  46. Broumi S, Deli I (2016) Correlation measure for neutrosophic refined sets and its application in medical diagnosis. Palestine J Math 5(1):135–143

    MathSciNet  MATH  Google Scholar 

  47. Majumdar P, Samant SK (2014) On similarity and entropy of neutrosophic sets. J Intell Fuzzy Syst 26(3):1245–1252

    MathSciNet  MATH  Google Scholar 

  48. Tian ZP, Zhang HY, Wang J, Wang JQ, Chen XH (2015) Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets. Int J Syst Sci. doi:10.1080/00207721.2015.1102359

    MATH  Google Scholar 

  49. Şahin R (2015) Cross-entropy measure on interval neutrosophic sets and its applications in multicriteria decision making. Neural Comput Appl. doi:10.1007/s00521-015-2131-5

    Google Scholar 

  50. Wu XH, Wang JQ, Peng JJ, Chen XH (2016) Cross-entropy and prioritized aggregation operator with simplified neutrosophic sets and their application in multi-criteria decision-making problems. Int J Fuzzy Syst. doi:10.1007/s40815-016-0180-2

    Google Scholar 

  51. Ye J (2015) Improved cosine similarity measures of simplified neutrosophic sets for medical diagnoses. Artif Intell Med 63(3):171–179

    Article  Google Scholar 

  52. Şahin R, Küçük A (2015) Subsethood measure for single valued neutrosophic sets. J Intell Fuzzy Syst 29(2):525–530

    Article  MATH  Google Scholar 

  53. Peng JJ, Wang JQ, Zhang HY, Chen XH (2014) An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets. Appl Soft Comput 25:336–346

    Article  Google Scholar 

  54. Zhang HY, Wang JQ, Chen XH (2016) An outranking approach for multi-criteria decision-making problems with interval-valued neutrosophic sets. Neural Comput Appl 27(3):615–627

    Article  Google Scholar 

  55. Zhang HY, Ji P, Wang JQ, Chen XH (2016) A neutrosophic normal cloud and its application in decision-making. Cogn Comput. doi:10.1007/s12559-016-9394-8

    Google Scholar 

  56. Ye J (2015) An extended TOPSIS method for multiple attribute group decision making based on single valued neutrosophic linguistic numbers. J Intell Fuzzy Syst 28(1):247–255

    MathSciNet  Google Scholar 

  57. Ye J (2014) Some aggregation operators of interval neutrosophic linguistic numbers for multiple attribute decision making. J Intell Fuzzy Syst 27(5):2231–2241

    MathSciNet  MATH  Google Scholar 

  58. Ma YX, Wang JQ, Jing Wang WuXH (2016) An interval neutrosophic linguistic multi-criteria group decision-making method and its application in selecting medical treatment options. Neural Comput Appl. doi:10.1007/s00521-016-2203-1

    Google Scholar 

  59. Ye J (2015) Multiple attribute group decision making based on interval neutrosophic uncertain linguistic variables. Int J Mach Learn Cybern. doi:10.1007/s13042-015-0382-1

    Google Scholar 

  60. 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 8:23–32

    Google Scholar 

  61. Broumi S, Smarandache F (2015) Single valued neutrosophic trapezoid linguistic aggregation operators based multi-attribute decision making. Bull Pure Appl Sci Math Stat 33(2):135–155

    Google Scholar 

  62. Yager RR (2008) Prioritized aggregation operators. Int J Approx Reason 48(1):263–274

    Article  MathSciNet  MATH  Google Scholar 

  63. Herrera F, Herrera-Viedma E, Verdegay JL (1996) A model of consensus in group decision-making under linguistic assessments. Fuzzy Sets Syst 79(1):73–87

    Article  MathSciNet  MATH  Google Scholar 

  64. Herrera F, Herrera-Viedma E (2000) Linguistic decision analysis: steps for solving decision problems under linguistic information. Fuzzy Sets Syst 115(1):67–82

    Article  MathSciNet  MATH  Google Scholar 

  65. Xu ZS (2006) A note on linguistic hybrid arithmetic averaging operator in multiple attribute decision-making with linguistic information. Group Decis Negot 15(6):593–604

    Article  Google Scholar 

  66. Bao GY, Lian XL, He M, Wang LL (2010) Improved two-tuple linguistic representation model based on new linguistic evaluation scale. Control Decis 25(5):780–784

    MathSciNet  Google Scholar 

  67. Kahneman D, Tversky A (1979) Prospect theory: an analysis of decision under risk. Econometrica 47(2):263–291

    Article  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  69. Tian ZP, Wang J, Wang JQ, Zhang HY (2016) Simplified neutrosophic linguistic multi-criteria group decision-making approach to green product development. Group Decis Negot. doi:10.1007/s10726-016-9479-5

    Google Scholar 

  70. Yager RR (2004) Choquet aggregation using order inducing variables. Int J Uncertain Fuzziness Knowl Based Syst 12(1):69–88

    Article  MathSciNet  MATH  Google Scholar 

  71. Zhou H, Wang JQ, Zhang HY (2016) Multi-criteria decision-making approaches based on distance measures for linguistic hesitant fuzzy sets. J Oper Res Soc. doi:10.1057/jors.2016.41

    Google Scholar 

Download references

Acknowledgments

The authors would like to thank the editors and anonymous reviewers for their helpful comments and suggestions that improved the paper. This work was supported by the National Natural Science Foundation of China (Nos. 71571193 and 71431006).

Author information

Authors and Affiliations

  1. School of Business, Central South University, Changsha, 410083, People’s Republic of China

    Zhang-peng Tian, Jing Wang, Hong-yu Zhang & Jian-qiang Wang

Authors
  1. Zhang-peng Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jing Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hong-yu Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jian-qiang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jian-qiang Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tian, Zp., Wang, J., Zhang, Hy. et al. Multi-criteria decision-making based on generalized prioritized aggregation operators under simplified neutrosophic uncertain linguistic environment. Int. J. Mach. Learn. & Cyber. 9, 523–539 (2018). https://doi.org/10.1007/s13042-016-0552-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-016-0552-9

Keywords

Search

Navigation