Advertisement

Some single-valued neutrosophic Bonferroni power aggregation operators in multiple attribute decision making

  • Guiwu Wei
  • Zuopeng Zhang
Original Research

Abstract

In this paper, we utilize power aggregation operators and Bonferroni mean to develop some single-valued neutrosophic Bonferroni power aggregation operators and single-valued neutrosophic geometric Bonferroni power aggregation operators. The prominent characteristics of these proposed operators are studied. Then, we use the SVNWBPM and SVNWGBPM operators to solve the single-valued neutrosophic multiple attribute decision making problems. Finally, a practical example for strategic suppliers’ selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Keywords

Multiple attribute decision making (MADM) Single-valued neutrosophic numbers SVNWBPM operator SVNWGBPM operator 

Notes

Acknowledgements

The work was supported by the National Natural Science Foundation of China under Grant nos. 61174149 and 71571128 and the Humanities and Social Sciences Foundation of Ministry of Education of the People’s Republic of China (17XJA630003) and the Construction Plan of Scientific Research Innovation Team for Colleges and Universities in Sichuan Province (15TD0004).

References

  1. Amato A, Di Martino B, Venticinque S (2014) Agents based multi-criteria decision-aid. J Ambient Intell Humaniz Comput 5(5):747–758CrossRefGoogle Scholar
  2. Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96zbMATHCrossRefGoogle Scholar
  3. Atanassov K (2000) Two theorems for intuitionistic fuzzy sets. Fuzzy Sets Syst 110:267–269MathSciNetzbMATHCrossRefGoogle Scholar
  4. Bajwa N, Fontem B, Sox CR (2016) Optimal product pricing and lot sizing decisions for multiple products with nonlinear demands. J Manag Anal 3(1):43–58Google Scholar
  5. Bellman R, Zadeh LA (1970) Decision making in a fuzzy environment. Manag Sci 17:141–164MathSciNetzbMATHCrossRefGoogle Scholar
  6. Biswas P, Pramanik S, Giri BC (2016) TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment. Neural Comput Appl 27:727–737CrossRefGoogle Scholar
  7. Chen TY (2016) An interval-valued intuitionistic fuzzy permutation method with likelihood-based preference functions and its application to multiple criteria decision analysis. Appl Soft Comput 42:390–409CrossRefGoogle Scholar
  8. Chiclana F, Herrera F, Herrera-Viedma E (2000) The ordered weighted geometric operator: Properties and application. In: Proceedings of 8th international conference on information processing and management of uncertainty in knowledge-based systems, Madrid, pp 985–991Google Scholar
  9. Gao H, Lu M, Wei GW, Wei Y (2018) Some novel Pythagorean fuzzy interaction aggregation operators in multiple attribute decision making. Fundamenta Informaticae 159(4):385–428MathSciNetzbMATHCrossRefGoogle Scholar
  10. Garg H (2016) A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem. J Intell Fuzzy Syst 31(1):529–540zbMATHCrossRefGoogle Scholar
  11. Levy R, Brodsky A, Luo J (2016) Decision guidance framework to support operations and analysis of a hybrid renewable energy system. J Manag Anal 3(4):285–304Google Scholar
  12. Li DF (2014) Decision and game theory in management with intuitionistic fuzzy sets. Studies in fuzziness and soft computing 308, Springer, New York, pp 1–441. ISBN 978-3-642-40711-6Google Scholar
  13. Li Y, Liu P, Chen Y (2016) Some single valued neutrosophic number Heronian mean operators and their application in multiple attribute group decision making. Informatica 27(1):85–110zbMATHCrossRefGoogle Scholar
  14. Liu PD, Wang YM (2014) Multiple attribute decision making method based on single-valued neutrosophic normalized weighted Bonferroni mean. Neural Comput Appl 25:2001–2010CrossRefGoogle Scholar
  15. Lu M, Wei GW, Alsaadi FE, Hayat T, Alsaedi A (2017) Bipolar 2-tuple linguistic aggregation operators in multiple attribute decision making. J Intell Fuzzy Syst 33(2):1197–1207zbMATHCrossRefGoogle Scholar
  16. Majumdar P, Samant SK (2014) On similarity and entropy of neutrosophic sets. J Intell Fuzzy Syst 26(3):1245–1252MathSciNetzbMATHGoogle Scholar
  17. Nayagam VLG, Sivaraman G (2011) Ranking of interval-valued intuitionistic fuzzy sets. Appl Soft Comput 11:3368–3372CrossRefGoogle Scholar
  18. Nikander J (2017) Suitability of papiNet-standard for straw biomass logistics. J Ind Inf Integr 6:11–21Google Scholar
  19. 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 25:336–346CrossRefGoogle Scholar
  20. Pourhassan MR, Raissi S (2017) An integrated simulation-based optimization technique for multi-objective dynamic facility layout problem. J Ind Inf Integr 8:49–58Google Scholar
  21. Ran LG, Wei GW (2015) Uncertain prioritized operators and their application to multiple attribute group decision making. Technol Econ Dev Econ 21(1):118–139CrossRefGoogle Scholar
  22. Sahin R (2014) Multi-criteria neutrosophic decision making method based on score and accuracy functions under neutrosophic environment. arXiv Preprint arXiv:1412.5202Google Scholar
  23. Sattarpour T, Nazarpour D, Golshannavaz S, Siano P (2018) A multi-objective hybrid GA and TOPSIS approach for sizing and siting of DG and RTU in smart distribution grids. J Ambient Intell Humaniz Comput 9(1):105–122CrossRefGoogle Scholar
  24. Smarandache F (1998) Neutrosophy: neutrosophic probability, set, and logic: analytic synthesis and synthetic analysis. American Research Press, Rehoboth, DE, USAzbMATHGoogle Scholar
  25. Smarandache F (1999) A unifying field in logics. Neutrosophy: neutrosophic probability, set and logic. American Research Press, RehobothzbMATHGoogle Scholar
  26. Smarandache F (2003) A unifying field in logics: neutrosophic logic. Neutrosophy, neutrosophic set, neutrosophic probability and statistics, 3rd edn. Xiquan, PhoenixzbMATHGoogle Scholar
  27. Smarandache F (2013) n-Valued refined neutrosophic logic and its applications in physics. Prog Phys 4:143–146Google Scholar
  28. Szmidt E, Kacprzyk J (2010) Dealing with typical values via Atanassov’s intuitionistic fuzzy sets. Int J Gen Syst 39:489–506MathSciNetzbMATHCrossRefGoogle Scholar
  29. Szmidt E, Kacprzyk J, Bujnowski P (2014) How to measure the amount of knowledge conveyed by Atanassov’s intuitionistic fuzzy sets. Inf Sci 257:276–285MathSciNetzbMATHCrossRefGoogle Scholar
  30. Wang H, Smarandache F, Zhang YQ, Sunderraman R (2005) Interval neutrosophic sets and logic: theory and applications in computing. Hexis, PhoenixzbMATHGoogle Scholar
  31. Wang H, Smarandache F, Zhang YQ, Sunderraman R (2010) Single valued neutrosophic sets. Multispace Multistruct 4:410–413zbMATHGoogle Scholar
  32. Wei GW (2010) GRA method for multiple attribute decision making with incomplete weight information in intuitionistic fuzzy setting. Knowl Based Syst 23:243–247CrossRefGoogle Scholar
  33. Wei GW (2015) Approaches to interval intuitionistic trapezoidal fuzzy multiple attribute decision making with incomplete weight information. Int J Fuzzy Syst 17(3):484–489MathSciNetCrossRefGoogle Scholar
  34. Wei GW (2016) Interval valued hesitant fuzzy uncertain linguistic aggregation operators in multiple attribute decision making. Int J Mach Learn Cybernet 7(6):1093–1114CrossRefGoogle Scholar
  35. Wei GW (2017) Interval-valued dual hesitant fuzzy uncertain linguistic aggregation operators in multiple attribute decision making. J Intell Fuzzy Syst 33(3):1881–1893zbMATHCrossRefGoogle Scholar
  36. Wei GW (2018a) Some similarity measures for picture fuzzy sets and their applications. Iran J Fuzzy Syst 15(1):77–89MathSciNetzbMATHGoogle Scholar
  37. Wei GW (2018b) Picture fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. Fundamenta Informaticae 157(3):271–320MathSciNetzbMATHCrossRefGoogle Scholar
  38. Wei GW, Wei Y (2018a) Similarity measures of Pythagorean fuzzy sets based on cosine function and their applications. Int J Intell Syst 33(3):634–652CrossRefGoogle Scholar
  39. Wei GW, Lu M (2018b) Pythagorean fuzzy power aggregation operators in multiple attribute decision making. Int J Intell Syst 33(1):169–186MathSciNetCrossRefGoogle Scholar
  40. Wei GW, Wang HJ, Lin R (2011) Application of correlation coefficient to interval-valued intuitionistic fuzzy multiple attribute decision-making with incomplete weight information. Knowl Inf Syst 26:337–349CrossRefGoogle Scholar
  41. Wei GW, Alsaadi FE, Hayat T, Alsaedi A (2016) Hesitant fuzzy linguistic arithmetic aggregation operators in multiple attribute decision making. Iranian Journal of Fuzzy Systems 13(4):1–16MathSciNetzbMATHGoogle Scholar
  42. Wei CM, Li ZP, Zou ZB (2017a) Ordering policies and coordination in a two-echelon supply chain with Nash bargaining fairness concerns. J Manag Anal 4(1):55–79Google Scholar
  43. Wei GW, Lu M, Alsaadi FE, Hayat T, Alsaedi A (2017b) Pythagorean 2-tuple linguistic aggregation operators in multiple attribute decision making. J Intell Fuzzy Syst 33(2):1129–1142zbMATHCrossRefGoogle Scholar
  44. Wei GW, Alsaadi FE, Hayat T, Alsaedi A (2018a) Picture 2-tuple linguistic aggregation operators in multiple attribute decision making. Soft Comput 22(3):989–1002zbMATHCrossRefGoogle Scholar
  45. Wei GW, Alsaadi FE, Hayat T, Alsaedi A (2018b) Bipolar fuzzy Hamacher aggregation operators in multiple attribute decision making. Int J Fuzzy Syst 20(1):1–12zbMATHMathSciNetCrossRefGoogle Scholar
  46. Wu J, Li L, Xu L (2014) A randomized pricing decision support system in electronic commerce. Decis Support Syst 58:43–52CrossRefGoogle Scholar
  47. 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. J Intell Fuzzy Syst 18:1104–1116CrossRefGoogle Scholar
  48. Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15(6):1179–1187CrossRefGoogle Scholar
  49. Xu L (2011) Information architecture for supply chain quality management. Int J Prod Res 49(1):183–198CrossRefGoogle Scholar
  50. Xu ZS, Da QL (2003) An overview of operators for aggregating information. Int J Intell Syst 18:953–969zbMATHCrossRefGoogle Scholar
  51. Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35:417–433MathSciNetzbMATHCrossRefGoogle Scholar
  52. Xu ZS, Yager RR (2010) Power-geometric operators and their use in group decision making. IEEE Trans Fuzzy Syst 18(1):94–105CrossRefGoogle Scholar
  53. Yager RR (1997) Multiple objective decision-making using fuzzy sets. Int J Man Mach Stud 9:375–382zbMATHCrossRefGoogle Scholar
  54. Yager RR (2001) The power average operator. IEEE Trans Syst Man Cybern Part A 31:724–731CrossRefGoogle Scholar
  55. Ye J (2010) Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment. Eur J Oper Res 205:202–204zbMATHCrossRefGoogle Scholar
  56. Ye J (2013) Multicriteria decision-making method using the correlation coefficient under single-value neutrosophic environment. Int J Gen Syst 42(4):386–394MathSciNetzbMATHCrossRefGoogle Scholar
  57. Ye J (2014a) A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets. J Intell Fuzzy Syst 26:2459–2466MathSciNetzbMATHGoogle Scholar
  58. Ye J (2014b) Single valued neutrosophic cross-entropy for multicriteria decision making problems. Appl Math Model 38(3):1170–1175MathSciNetzbMATHCrossRefGoogle Scholar
  59. Ye J (2015) Improved cosine similarity measures of simplified neutrosophic sets for medical diagnoses. Artif Intell Med 63:171–179CrossRefGoogle Scholar
  60. Ye J (2016a) Projection and bidirectional projection measures of single valued neutrosophic sets and their decision-making method for mechanical design schemes. J Exp Theor Artif Intell 6:1–10Google Scholar
  61. Ye J (2016b) Similarity measures of intuitionistic fuzzy sets based on cosine function for the decision making of mechanical design schemes. J Intell Fuzzy Syst 30(1):151–158zbMATHCrossRefGoogle Scholar
  62. Ye J (2017a) Single valued neutrosophic similarity measures based on cotangent function and their application in the fault diagnosis of steam turbine. Soft Comput 21:817–825zbMATHCrossRefGoogle Scholar
  63. Ye J (2017b) Single-valued neutrosophic clustering algorithms based on similarity measures. J Classif 2017 34:148–162MathSciNetzbMATHGoogle Scholar
  64. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–356zbMATHCrossRefGoogle Scholar
  65. Zhang HY, Wang JQ, Chen XH (2014) Interval neutrosophic sets and their application in multicriteria decision making problems. Sci Word J 645953:15Google Scholar
  66. Zhao XF, Wei GW (2013) Some intuitionistic fuzzy Einstein hybrid aggregation operators and their application to multiple attribute decision making. Knowl Based Syst 37:472–479CrossRefGoogle Scholar
  67. Zhu B, Xu ZS, Xia MM (2012) Hesitant fuzzy geometric Bonferroni means. Inf Sci 205:72–85MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of BusinessSichuan Normal UniversityChengduChina
  2. 2.School of Business and EconomicsState University of New YorkPlattsburghUSA

Personalised recommendations