Skip to main content
SpringerLink
Log in

An Extension of ARAS Methodology for Multi-criteria Group Decision-Making Problems within Probability Multi-valued Neutrosophic Sets

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

Probability multi-valued neutrosophic sets (PMVNSs) can depict the preference and hesitancy of decision makers (DMs) simultaneously, and utility-based additive ratio assessment (ARAS) can effectively evaluate and rank feasible alternatives. In order to make optimal decision making under the environment of the PMVNSs, in this paper, an extended ARAS methodology for multi-criteria group decision making (MCGDM) is developed. Firstly, we propose probability multi-valued neutrosophic normalized weighted Bonferroni distance (PMVNNWBD) to measure the closeness of weighted probability multi-valued neutrosophic numbers (PMVNNs). Then, an entropy measure for PMVNSs is proposed to describe the inaccuracy degree of PMVNSs and to derive the weights of DMs. Further, considering the relationship between criteria, we construct a modified maximizing deviation model based on PMVNNWBD to obtain criteria weights. Moreover, an extended ARAS method for MCGDM is established to handle PMVNSs based on the obtained weight information of DMs and criteria. Finally, the feasibility and superiority of the proposed approach are verified by a case study concerning third-party logistics (3PLs) supplier selection, and sensitive analysis of different parameters shows our proposed approach is flexible.

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

  1. Liu, P., Chen, S.: Multiattribute group decision making based on intuitionistic 2-tuple linguistic information. Inf. Sci. 430, 599–619 (2018)

    Article  MathSciNet  Google Scholar 

  2. Liu, P.: A weighted aggregation operators multi-attribute group decision-making method based on interval-valued trapezoidal fuzzy numbers. Expert Syst. Appl. 38(1), 1053–1060 (2011)

    Article  MathSciNet  Google Scholar 

  3. Liu, P.: Some Hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making. IEEE Trans. Fuzzy Syst. 22(1), 83–97 (2014)

    Article  Google Scholar 

  4. Smarandache, F.: A Unifying Field in Logics Neutrosophy: Neutrosophic Probability, Set and Logic. American Research Press, Rehoboth (1998)

    MATH  Google Scholar 

  5. Zadeh, L.: Fuzzy sets. Inform. Control 8(3), 338–353 (1965)

    Article  Google Scholar 

  6. Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)

    Article  MATH  Google Scholar 

  7. Chen, T.: Multiple criteria group decision-making with generalized interval-valued fuzzy numbers based on signed distances and incomplete weights. Appl. Math. Model. 36(7), 3029–3052 (2012)

    Article  MATH  Google Scholar 

  8. Xu, Z.: Intuitionistic fuzzy aggregation operators. IEEE Trans. Fuzzy Syst. 15(6), 1179–1187 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Shenify, M., Mazarbhuiya, F.: The expected value of a fuzzy number. Int. J. Intell. Sci. 5, 1–5 (2015)

    Article  Google Scholar 

  10. Chen, T., Wang, H., Lu, Y.: A multicriteria group decision-making approach based on interval-valued intuitionistic fuzzy sets: a comparative perspective. Expert Syst. Appl. 38(6), 7647–7658 (2011)  

    Article  Google Scholar 

  11. Ansaria, A., Biswasb, R., Aggarwalc, S.: Neutrosophic classifier: an extension of fuzzy classifer. Appl. Soft Comput. 13(1), 563–573 (2013)

    Article  Google Scholar 

  12. Wang, X., Ashfaq, R., Fu, A.: Fuzziness based sample categorization for classifier performance improvement. J. Intell. Fuzzy Syst. 29(3), 1185–1196 (2015)

    Article  MathSciNet  Google Scholar 

  13. Wang, X., Xing, H., Li, Y., Hua, Q., Dong, C., Pedrycz, W.: A study on relationship between generalization abilities and fuzziness of base classifiers in ensemble learning. IEEE Trans. Fuzzy Syst. 23(5), 1638–1654 (2005)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  16. Wu, X., Wang, J., Peng, J., Chen, X.: Cross-entropy and prioritized aggregation operator with simplified neutrosophic sets and their application in multi-criteria decision-making problems. Int. J. Fuzzy Syst. 18(6), 1104–1116 (2016)

    Article  Google Scholar 

  17. Wang, H., Smarandache, F., Zhang, Y., Sunderraman, R.: Single valued neutrosophic sets. Multispace Multistruct. 4, 410–413 (2010)

    MATH  Google Scholar 

  18. Wang, L., Zhang, H., Wang, J.: Frank Choquet Bonferroni mean operators of bipolar neutrosophic sets and their application to multi-criteria decision-making problems. Int. J. Fuzzy Syst. 20(1), 13–28 (2018)

    Article  MathSciNet  Google Scholar 

  19. Liu, P., Khan, Q., Ye, J., Mahmood, T.: Group decision-making method under hesitant interval neutrosophic uncertain linguistic environment. Int. J. Fuzzy Syst. 20(7), 2337–2353 (2018)

    Article  Google Scholar 

  20. Zhou, H., Wang, J., Zhang, H.: Grey stochastic multi-criteria decision-making approach based on prospect theory and distance measures. J. Grey Syst. 29(1), 15–33 (2017)

    Google Scholar 

  21. Wang, J., Li, X.: TODIM method with multi-valued neutrosophic sets. Control Decis. 30(6), 1139–1142 (2015)

    MathSciNet  Google Scholar 

  22. Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25(6), 529–539 (2010)

    MATH  Google Scholar 

  23. Şahin, R., Liu, P.: Correlation coefficient of single-valued neutrosophic hesitant fuzzy sets and its applications in decision making. Neural Comput. Appl. 28(6), 1387–1395 (2017)

    Article  Google Scholar 

  24. Liu, P., Zhang, L., Liu, X., Wang, P.: Multi-valued neutrosophic number Bonferroni mean operators and their application in multiple attribute group decision making. Int. J. Inf. Technol. Decis. Mak. 15(5), 1181–1210 (2016)

    Article  Google Scholar 

  25. Peng, J., Wang, J., Yang, W.: A multi-valued neutrosophic qualitative flexible approach based on likelihood for multi-criteria decision-making problems. Int. J. Syst. Sci. 48(2), 425–435 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  26. Zeng, W., Li, D., Yin, Q.: Weighted Interval-valued hesitant fuzzy sets and its application in group decision making. Int. J. Fuzzy Syst. 21(2), 421–432 (2019)

    Article  Google Scholar 

  27. Zhao, M., Gao, Q., Fang, J., Xiao, Q.: An approach to consensus measure based on possibility degrees of PLTSs in group decision making. Int. J. Fuzzy Syst. 20(7), 2257–2272 (2018)

    Article  Google Scholar 

  28. Zhang, X.: A novel probabilistic linguistic approach for large-scale group decision making with incomplete weight information. Int. J. Fuzzy Syst. 20(7), 2245–2256 (2018)

    Article  Google Scholar 

  29. Liang, D., Kobina, A., Quan, W.: Grey relational analysis method for probabilistic linguistic multi-criteria group decision-making based on geometric Bonferroni mean. Int. J. Fuzzy Syst. 20(7), 2234–2244 (2018)

    Article  Google Scholar 

  30. Peng, H., Zhang, H., Wang, J.: Probability multi-valued neutrosophic sets and its application in multi-criteria group decision-making problems. Neural Comput. Appl. 30(2), 563–583 (2018)

    Article  Google Scholar 

  31. Liu, P., Cheng, S., Zhang, Y.: An extended multi-criteria group decision-making PROMETHEE method based on probability multi-valued neutrosophic sets. Int. J. Fuzzy Syst. 21(2), 388–406 (2019)

    Article  Google Scholar 

  32. Arditi, D., Gunaydin, H.: Perceptions of process quality in building projects. J. Manag. Eng. 15(2), 43–53 (1999)

    Article  Google Scholar 

  33. MacCrimmon K.: Decision making among multiple-attribute alternatives: a survey and consolidated approach. RAND CORP SANTA MONICA CA (1968)

  34. Srinivasan, V., Shocker, A.: Linear programming techniques for multidimensional analysis of preferences. Psychometrika 38(3), 337–369 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  35. Zavadskas, E., Turskis, Z.: A new additive ratio assessment (ARAS) method in multicriteria decision-making. Technol. Econ. Dev. Econ. 16(2), 159–172 (2010)

    Article  Google Scholar 

  36. Turskis, Z., Zavadskas, E.: A new fuzzy Additive Ratio Assessment method (ARAS-F).Case study: the analysis of fuzzy multiple criteria in order to select the logistic centers location. Transport 25(4), 423–432 (2010)

    Article  Google Scholar 

  37. Turskis, Z., Zavadskas, E.: A novel method for multiple criteria analysis: grey additive ratio assessment (ARAS-G) method. Informatica 21(4), 597–610 (2010)

    MathSciNet  Google Scholar 

  38. Balezentiene, L., Kusta, A.: Reducing greenhouse gas emissions in grassland ecosystems of the central Lithuania: multi-criteria evaluation on a basis of the ARAS method. Sci. World J. 2012, 1–11 (2012)

    Article  Google Scholar 

  39. Büyüközkan G., Göçer F.: An extension of ARAS methodology based on interval valued intuitionistic fuzzy group decision making for digital supply chain. In: 2017 IEEE international conference on fuzzy systems (FUZZ-IEEE). IEEE, pp. 1–6 (2017)

  40. Zhou, W., He, J.: Intuitionistic fuzzy normalized weighted Bonferroni mean and its application in multicriteria decision making. J. Appl. Math. 2012, 1–22 (2012)

    MathSciNet  MATH  Google Scholar 

  41. Wang, L., Peng, J., Wang, J.: A multi-criteria decision-making framework for risk ranking of energy performance contracting project under picture fuzzy environment. J. Clean. Prod. 191, 105–118 (2018)

    Article  Google Scholar 

  42. Zadeh L.: Fuzzy sets and systems. In: Proc. Symp. on Systems Theory, Polytechnic Institute of Brooklyn, New York, 1965

  43. Ji, Y., Huang, G., Sun, W.: Risk assessment of hydropower stations through an integrated fuzzy entropy-weight multiple criteria decision making method: a case study of the Xiangxi River. Expert Syst. Appl. 42(12), 5380–5389 (2015)

    Article  Google Scholar 

  44. Wang, J., Wang, J.Q., Zhang, H.: A likelihood-based TODIM approach based on multi-hesitant fuzzy linguistic information for evaluation in logistics outsourcing. Comput. Ind. Eng. 99, 287–299 (2016)

    Article  Google Scholar 

  45. Ji, P., Zhang, H., Wang, J.: A projection-based TODIM method under multi-valued neutrosophic environments and its application in personnel selection. Neural Comput. Appl. 29(1), 221–234 (2018)

    Article  Google Scholar 

  46. Wan, S., Wang, F., Dong, J.: A novel group decision making method with intuitionistic fuzzy preference relations for RFID technology selection. Appl. Soft Comput. 38, 405–422 (2016)

    Article  Google Scholar 

  47. Yazdani, M., Zarate, P., Coulibaly, A., Zavadskas, E.: A group decision making support system in logistics and supply chain management. Expert Syst. Appl. 88, 376–392 (2017)

    Article  Google Scholar 

Download references

Acknowledgements

This paper is supported by the National Natural Science Foundation of China (Nos. 71771140 and 71471172), the Special Funds of Taishan Scholars Project of Shandong Province (No. ts201511045),

figure c

, and Shandong Provincial Social Science Planning Project (Nos. 17BGLJ04, 16CGLJ31 and 16CKJJ27).

Author information

Authors and Affiliations

  1. School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, 250014, Shandong, China

    Peide Liu & Shufeng Cheng

Authors
  1. Peide Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shufeng Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peide Liu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, P., Cheng, S. An Extension of ARAS Methodology for Multi-criteria Group Decision-Making Problems within Probability Multi-valued Neutrosophic Sets. Int. J. Fuzzy Syst. 21, 2472–2489 (2019). https://doi.org/10.1007/s40815-019-00737-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-019-00737-4

Keywords

Search

Navigation