Advertisement

Neural Computing and Applications

, Volume 29, Issue 9, pp 553–564 | Cite as

Linear assignment method for interval neutrosophic sets

  • Wei Yang
  • Jiarong Shi
  • Yongfeng Pang
  • Xiuyun Zheng
Original Article

Abstract

Interval neutrosophic sets are the generalization of interval-valued intuitionistic fuzzy sets by considering the indeterminacy membership. A new multiple attribute decision-making method based on the interval neutrosophic sets and linear assignment has been developed, in which correlation of information has been considered by using the Choquet integral. We first develop the generalized interval neutrosophic fuzzy correlated averaging operator. Then, we generalize linear assignment method to accommodate the interval neutrosophic sets based on the Choquet integral. Finally, we apply it to solve the problem of selecting invest company to illustrate feasibility and practical advantages of the new algorithm in decision making. The comparison of new method with some other methods has been conducted.

Keywords

Multiple attribute decision making Interval neutrosophic set Linear assignment method Choquet integral Aggregation operator 

Notes

Acknowledgments

The authors would like to express appreciation to the anonymous reviewers for their very helpful comments on improving the paper. This work is partly supported by National Natural Science Foundation of China (Nos. 11401457, 61403298), Postdoctoral Science Foundation of China (2015M582624), Shaanxi Province Natural Science Fund of China (Nos. 2014JQ1019, 2014JM1010), Shaanxi Provincial Education Department fund of China (No. 16JK1435).

References

  1. 1.
    Zadeh LA (1965) Control Inf. Fuzzy sets 8(3):338–353Google Scholar
  2. 2.
    Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96CrossRefzbMATHGoogle Scholar
  3. 3.
    Atanassov K, Gargov G (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31(3):343–349MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Torra V, Narukawa Y (2009) On hesitant fuzzy sets and decision. In: The 18th IEEE international conference on fuzzy systems, Jeju Island, Korea, pp 1378–1382Google Scholar
  5. 5.
    Chiclana F, Herrera F, Herrera-Viedma E (2011) Integrating multiplicative preference relations in a multipurpose decision-making model based on fuzzy preference relations. Fuzzy Sets Syst 122:277–291MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Smarandache F (1998) A unifying field in logics. Neutrosophy: neutrosophic probability, set and logic. American Research Press, RehobothzbMATHGoogle Scholar
  7. 7.
    Liu PD, Tang GL (2016) Some power generalized aggregation operators based on the interval neutrosophic sets and their application to decision making. J Intell Fuzzy Syst 30(5):2517–2528MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Wang H, Smarandache F, Zhang Y, Sunderraman R (2005) Single valued neutrosophic sets. In: Proceedings of 10th international conference on fuzzy theory and technology. Salt Lake City, UtahGoogle Scholar
  9. 9.
    Maji PK (2013) Neutrosophic soft set. Ann Fuzzy Math Inform 5(1):157–168MathSciNetzbMATHGoogle Scholar
  10. 10.
    Guo YH, Şengür A (2014) A novel image segmentation algorithm based on neutrosophic similarity clustering. Appl Soft Comput 25:391–398CrossRefGoogle Scholar
  11. 11.
    Şengür A, Guo YH (2011) Color texture image segmentation based on neutrosophic set and wavelet transformation. Comput Vis Image Underst 115(8):1134–1144CrossRefGoogle Scholar
  12. 12.
    Maji PK (2015) An application of weighted neutrosophic soft sets in a decision-making problem. Springer Proc Math Stat 125:215–223CrossRefGoogle Scholar
  13. 13.
    Zhang L, Zhang M (2015) Segmentation of blurry images based on interval neutrosophic set. J Inform Comput Sci 12(7):2769–2777CrossRefGoogle Scholar
  14. 14.
    Kazim H, Fatih TM (2014) Segmentation of SAR images using improved artificial bee colony algorithm and neutrosophic set. Appl Soft Comput 21:433–443CrossRefGoogle Scholar
  15. 15.
    Wang H, Smarandache F, Zhang YQ, Sunderraman R (2005) Interval neutrosophic sets and logic: theory and applications in computing. Hexis, Phoenix, AZGoogle Scholar
  16. 16.
    Ye J (2015) An extended TOPSIS method for multiple attribute group decision making based on single valued neutrosophic linguistic numbers. J Intell Fuzzy Syst 28:247–255MathSciNetGoogle Scholar
  17. 17.
    Ye J (2015) Trapezoidal neutrosophic set and its application to multiple attribute decision-making. Neural Comput Appl 26:1157–1166CrossRefGoogle Scholar
  18. 18.
    Sun HX, Yang HX, Wu JZ, Ouyang Y (2015) Interval neutrosophic numbers Choquet integral operator for multi-criteria decision making. J Intell Fuzzy Syst 28:2443–2455MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Sun HC, Sun M (2015) Simplified neutrosophic weighted Maclaurin symmetric mean and its application to supply chain management. ICIC Express Lett 9(12):3221–3227Google Scholar
  20. 20.
    Zhao AW, Du JG, Guan HJ (2015) Interval valued neutrosophic sets and multi-attribute decision-making based on generalized weighted aggregation operator. J Intell Fuzzy Syst 29:2697–2706CrossRefzbMATHGoogle Scholar
  21. 21.
    Liu PD, Chu YC, Li YW, Chen YB, Y.B. Chen YB (2014) Some generalized neutrosophic number hamacher aggregation operators and their application to group decision making. Int J Fuzzy Syst 16(2):242–255Google Scholar
  22. 22.
    Liu PD, Shi LL (2015) The generalized hybrid weighted average operator based on interval neutrosophic hesitant set and its application to multiple attribute decision making. Neural Comput Appl 26(2):457–471CrossRefGoogle Scholar
  23. 23.
    Ye J (2015) Multiple attribute decision-making method based on the possibility degree ranking method and ordered weighted aggregation operators of interval neutrosophic numbers. J Intell Fuzzy Syst 28:1307–1317MathSciNetGoogle Scholar
  24. 24.
    Ye J (2013) Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment. Int J Gen Syst 42(4):386–394MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Ye J (2014) Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making. J Intell Fuzzy Syst 26:165–172zbMATHGoogle Scholar
  26. 26.
    Ye J (2014) Single valued neutrosophic cross-entropy for multicriteria decision making problems. Appl Math Model 38:1170–1175MathSciNetCrossRefGoogle Scholar
  27. 27.
    Tian ZP, Zhang HY, Wang J, Wang JQ, Chen XH (2016) Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets. Int J Syst Sci 47(15):3598–3608CrossRefzbMATHGoogle Scholar
  28. 28.
    Şahin R, Küçük A (2014) On similarity and entropy of neutrosophic soft sets. J Intell Fuzzy Syst 27:2417–2430MathSciNetzbMATHGoogle Scholar
  29. 29.
    Majumdar P, Samant SK (2014) On similarity and entropy of neutrosophic sets. J Intell Fuzzy Syst 26:1245–1252MathSciNetzbMATHGoogle Scholar
  30. 30.
    Rdvan A (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
  31. 31.
    Karaaslan F (2016) Correlation coefficients of single-valued neutrosophic refined soft sets and their applications in clustering analysis. Neural Comput Appl. doi: 10.1007/s00521-016-2209-8
  32. 32.
    Karaaslan F (2016) Correlation coefficient between possibility neutrosophic soft sets. Math Sci Lett 5(1):71–74MathSciNetCrossRefGoogle Scholar
  33. 33.
    Yang HL, Guo ZL, She YH, Liao XW (2016) On single valued neutrosophic relations. J Intell Fuzzy Syst 30(2):1045–1056CrossRefzbMATHGoogle Scholar
  34. 34.
    Biswas P, Pramanik S, Giri BC (2016) TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment. Neural Comput Appl 27(3):727–737CrossRefGoogle Scholar
  35. 35.
    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
  36. 36.
    Bernardo JJ, Blin JM (1977) A programming model of consumer choice among multi-attributed brands. J Consum Res 4(2):111–118CrossRefGoogle Scholar
  37. 37.
    Lin CJ, Wen UP (2004) A labeling algorithm for the fuzzy assignment problem. Fuzzy Sets Syst 142(3):373–391MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Liu HT, Wang WK (2009) An integrated fuzzy approach for provider evaluation and selection in third-party logistics. Expert Syst Appl 36:4387–4398CrossRefGoogle Scholar
  39. 39.
    Bashiri M, Badri H, Hejazi TH (2011) Selecting optimum maintenance strategy by fuzzy interactive linear assignment method. Appl Math Model 35:152–164MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Bashiri M, Badri H (2011) A group decision making procedure for fuzzy interactive linear assignment programming. Expert Syst Appl 38:5561–5568CrossRefGoogle Scholar
  41. 41.
    Chen TY (2013) A linear assignment method for multiple-criteria decision analysis with interval type-2 fuzzy sets. Appl Soft Comput 13:2735–2748CrossRefGoogle Scholar
  42. 42.
    Chen TY (2014) The extended linear assignment method for multiple criteria decision analysis based on interval-valued intuitionistic fuzzy sets. Appl Math Model 38:2101–2117MathSciNetCrossRefGoogle Scholar
  43. 43.
    Jahan A, Ismail MY, Mustapha F, Sapuan SM (2010) Material selection based on ordinal data. Mater Des 31(7):3180–3187CrossRefGoogle Scholar
  44. 44.
    Sugeno M (1974) Theory of fuzzy integrals and applications. Diss, Tokyo Institute of TechnologyGoogle Scholar
  45. 45.
    Choquet G (1953) Theory of capacities. Annales del Institut Fourier 5:131–295MathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    Yager RR (2003) Induced aggregation operators. Fuzzy Sets Syst 137:59–69MathSciNetCrossRefzbMATHGoogle Scholar
  47. 47.
    Grabisch M, Labreuche C (2008) A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. OR 6:1–44MathSciNetzbMATHGoogle Scholar
  48. 48.
    Meng FY, Zhang Q (2014) Induced continuous Choquet integral operators and their application to group decision making. Comput Ind Eng 68:42–53CrossRefGoogle Scholar
  49. 49.
    Wang Z, Klir G (1992) Fuzzy measure theory. Plenum press, New YorkCrossRefzbMATHGoogle Scholar
  50. 50.
    Grabisch M (1997) K-order additive discrete fuzzy measures and their representation. Fuzzy Sets Syst 92:167–189MathSciNetCrossRefzbMATHGoogle Scholar
  51. 51.
    Yang W (2013) Induced quasi-arithmetic uncertain linguistic aggregation operator. Int J Uncertain Fuzziness Knowl Based Syst 21(1):55–77CrossRefzbMATHGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2016

Authors and Affiliations

  • Wei Yang
    • 1
  • Jiarong Shi
    • 1
  • Yongfeng Pang
    • 1
  • Xiuyun Zheng
    • 1
  1. 1.Xi’an University of Architecture and TechnologyXi’anPeople’s Republic of China

Personalised recommendations