Trapezoidal neutrosophic aggregation operators and their application to the multi-attribute decision-making process

Document Type : Article

Authors

1 Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University, Midnapore 721102, India

2 Department of Mathematics, Faculty of Sciences, Cankr Karatekin University, Cankr, Turkey

3 School of Business, Central South University, Changsha 410083, PR China

Abstract

The aim of this paper is to introduce interval trapezoidal neutrosophic set which is a combination
of trapezoidal fuzzy numbers and interval neutrosophic set. The paper presents some operational
rules, the score and accuracy functions of interval trapezoidal neutrosophic numbers. Then, some
aggregating operators under interval trapezoidal neutrosophic information which are called interval
trapezoidal neutrosophic number weighted arithmetic averaging (ITNNWAA) operator and interval
trapezoidal neutrosophic number weighted geometric averaging (ITNNWGA) operator, are proposed,
and their properties are investigated in detail. Furthermore, based on these operators a multi-attribute
decision making method is developed. Finally, a numerical example is presented to illustrate the
application and effectiveness of the proposed method.

Keywords

Main Subjects

References

References:
1. Zadeh, L.A. "Fuzzy sets", Information and Control, 8, pp. 338-353 (1965).
2. Turksen, I.B. "Interval valued fuzzy sets based on normal forms", Fuzzy Sets and Systems, 20, pp. 191- 210 (1989).
3. Atanassov, K.T. "Intuitionistic fuzzy sets: Theory and applications", Studies in Fuzziness and Soft Computing, 35, Physica-Verlag, Heidelberg/New York (1999).
4. Atanassov, K.T. and Gargov, G. "Interval valued intuitionistic fuzzy sets", Fuzzy Sets and Systems, 31, pp. 343-349 (1989).
5. Gau, W.L. and Buehrer, D.J. "Vague sets", IEEE Trans Syst ManCybern, 23, pp. 610-614 (1993).
6. Bustince, H. and Burillo, P. "Vague sets are intuitionistic fuzzysets", Fuzzy Sets and Systems, 79, pp. 403- 405 (1996).
7. Smarandache, F., A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic, American Research Press, Rehoboth (1999).
8. Smarandache, F., Neutrosophy. Neutrosophic Probability, Set, and Logic, ProQuest Information and Learning, Ann Arbor, Michigan, USA, p. 105 (1998).
9. Wang, H., Smarandache, F., Zhang, Y.Q., and Sunderraman, R. "Single valued neutrosophic sets", Multispace and Multistructure, 4, pp. 410-413 (2010).
10. Sahin, R. and Liu, P.D. "Correlation coefficients of single valued neutrosophic hesitant fuzzy sets and their applications in decision making", Neural Computing and Applications, 28(6), pp. 1387-1395 (2017).
11. Ye, J. "Multi criteria decision-making method using the correlation coefficient under single-valued neutrosophic environment", International Journal of General Systems, 42(4), pp. 386-394 (2013).
12. Ye, J. "Single valued neutrosophic cross entropy for multi criteria decision making problems, Applied Mathematical Modelling, 38, pp. 1170-1175 (2013).
13. Wang, H., Smarandache, F., Zhang, Y.Q., and Sunderraman, R., Interval Neutrosophic Sets and Logic: Theory and Applications in Computing, Hexis, Phoenix, AZ (2005).
14. Tian, Z.P., Wang, J., Wang, J.Q., and Zhang, H.Y. "Simplified neutrosophic linguistic multi-criteria group decision-Making approach to green product development", Group Decision and Negotiation, 26(3), pp. 597-627 (2017).
15. Tian, Z.P., Zhang, H., Wang, J., Wang, J.Q., and Chen, X. "Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets", International Journal of Systems Science, 47(15), pp. 3598-3608 (2016).
16. Ye, J. "Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making", Journal of Intelligent and Fuzzy Systems, 26, pp. 165-172 (2014).
17. Liang, R.X., Wang, J.Q., and Li, L. "Multi-criteria group decision making method based on interdependent inputs of single valued trapezoidal neutrosophic information", Neural Computing and Applications, 30(1), pp. 241-260 (2018).
18. Peng, H.G., Zhang, H.Y., andWang, J.Q. "Probability multi-valued neutrosophic sets and its application in multi-criteria group decision-making problems", Neural Computing and Applications, 30(2), pp. 536-583 (2018).
19. Wang, J.Q., Yang, Y., and Lin, L. "Multi-criteria decision-making method based on single valued neutrosophic linguistic Maclaurin symmetric mean operators", Neural Computing and Applications, 30(5), pp. 1529-1547 (2018).
20. Yu, S.M., Wang, J., and Wang, J.Q. "An extended TODIM approach with intuitionistic linguistic numbers", International Transactions in Operational Research, Multiple Criteria Decision Making: Current Challenges and Future Trends, 25(3), pp. 781-805 (2018).
21. Karaaslan, F. "Possibility neutrosophic soft sets and PNS-decision making method", Applied Soft Computing, 54, pp. 403-414 (2017).
22. Karaaslan, F. "Correlation coefficients of single-valued neutrosophic refined soft sets and their applications in clustering analysis", Neural Computing and Applications, 28(9), pp. 2781-2793 (2017).
23. Karaaslan, F. "Multi-criteria decision making method based on similarity measures under single-valued neutrosophic refined and interval neutrosophic refined environments", International Journal of Intelligent Systems, 33(5), pp. 928-952 (2018).
24. Herrera, F., Herrera-Viedma, E., and Chiclana, F. "A study of the origin and uses of the ordered weighted geometric operator in multicriteria decision making", International Journal of Intelligent Systems, 18(6), pp. 689-707 (2003).
25. Gao, H., Wei, G.W., and Huang, Y. "Dual hesitant bipolar fuzzy Hamacher prioritized aggregation operators in multiple attribute decision making", IEEE Access, 6(1), pp. 11508-11522 (2018).
26. Xu, Z.S. and Yager, R.R. "Some geometric aggregation operators based on intuitionistic fuzzy sets", International Journal of General System, 35, pp. 417-433 (2006).
27. Xu, Z.S. "Intuitionistic fuzzy aggregation operators", IEEE Transactions on Fuzzy Systems, 15(6), pp. 1179-1187 (2007).
28. Xu, Z.S. "Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making", Control and Decision, 22(2), pp. 215-219 (2007).
29. Liu, P., Zhang, X., and Jin, F. "A multi-attribute group decision making method based on intervalvalued trapezoidal fuzzy numbers hybrid harmonic averaging operators", Journal of Intelligent and Fuzzy Systems, 23(5), pp. 159-168 (2012).
30. Liu, H.W. and Wang, G.J. "Multi-criteria methods based on intuitionistic fuzzy sets", European Journal of Operational Research, 179, pp. 220-233 (2007).
31. Zhi, P. and Li, Z. "A novel approach to multi-attribute decision making based on intuitionistic fuzzy sets", Expert Systems with Applications, 39, pp. 2560-2566 (2007).
32. Wei, G.W., Gao, H., and Wei, Y. "Some q-rung orthopair fuzzy Heronian mean operators in multiple attribute decision making", International Journal of Intelligent Systems, 33(7), pp. 1426-1458 (2018).
33. Wei, G.W., Lu, M., Tang, X., and Wei, Y. "Pythagorean hesitant fuzzy Hamacher aggregation operators and their application to multiple attribute decision making", International Journal of Intelligent Systems, 33(6), pp. 1197-1233 (2018).
34. Liu, P. and Jin, F. "Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making", Information Sciences, 205, pp. 58-71 (2012).
35. Wang, J., Wei, G.W., and Wei, Y. "Models for green supplier selection with some 2-tuple linguistic neutrosophic number Bonferroni mean operators", Symmetry, 10(5), p. 131 (2018). DOI: 10.3390/sym10050131.
36. Wu, S., Wang, J., Wei, G.W., and Wei, Y. "Research on construction engineering project risk assessment with some 2-tuple linguistic neutrosophic Hamy mean operators", Sustainability, 10(5), p. 1536 (2018). https://doi.org/10.3390/su10051536.
37. Liu, P. "Some Hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making", IEEE Transactions on Fuzzy Systems, 22(1), pp. 83-97 (2014). DOI: 10.1109/TFUZZ.2013.2248736.
38. Liu, P. "Some generalized dependent aggregation operators with intuitionistic linguistic numbers and their application to group decision making", Journal of Computer and System Sciences, 79(1), pp. 131-143 (2013).
39. Garg, H., Agarwal, N., and Tripathi, A. "Some improved interactive aggregation operators under interval-valued intuitionistic fuzzy environment and its application to decision making process", Scientia Iranica E, 24(5), pp. 2581-2604 (2017).
40. Garg, H. "Generalized intuitionistic fuzzy multiplicative interactive geometric operators and their application to multiple criteria decision making", International Journal of Machine Learning and Cybernetics, 7(7), pp. 1075-1092 (2016).
41. Garg, H. "A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision-making processes", International Journal of Intelligent Systems, 31(12), pp. 1234-1253 (2016).
42. Garg, H. "A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making", International Journal of Intelligent Systems, 31(9), pp. 886-920 (2016).
43. Garg, H. "Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm and their application to decision making", Computer and Industrial Engineering, 101, pp. 53-69 (2016).
44. Arora, R. and Garg, H. "Prioritized averaging/ geometric aggregation operators under the intuitionistic fuzzy soft set environment", Scientia Iranica, E, 25(1), pp. 662-687 (2018).
45. Jana, C. and Pal, M. "Application of bipolar intuitionistic fuzzy soft sets in decision making problem", International Journal of Fuzzy System Applications, 7(3), pp. 32-55 (2018).
46. Wei, G.W., Zhao, X.F. and Lin, R. "Some induced aggregating operators with fuzzy number intuitionistic fuzzy information and their applications to group decision making", International Journal of Computational Intelligence Systems, 3(1), pp. 84-95 (2010).
47. Ye, J. "A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets", Journal of Intelligent and Fuzzy Systems, 26, pp. 2459-2466 (2014).
48. Liu, F. and Yuan, X.H. "Fuzzy number intuitionistic fuzzy set", Fuzzy Systems and Mathematics, 21(1), pp. 88-91 (2007).
49. Wang, X.F. "Fuzzy number intuitionistic fuzzy arithmetic aggregation operators", International Journal of Fuzzy Systems, 10(2), pp. 104-111 (2008).
50. Liu, P. and Jin, F. "A multi-attribute group decisionmaking method based on weighted geometric aggregation operators of interval-valued trapezoidal fuzzy numbers", Applied Mathematical Modelling, 36(6), pp. 2498-2509 (2012).
51. Liu, P. "A weighted aggregation operators multiattribute group decision-making method based on interval-valued trapezoidal fuzzy numbers", Expert Systems with Applications, 38(1), pp. 1053-1060 (2011).
52. Wu, J. and Liu, Y. "An approach for multiple attribute group decision making problems with interval-valued intuitionistic trapezoidal fuzzy numbers", Computers and Industrial Engineering, 66, pp. 311-324 (2013).
53. Ye, J. "Prioritized aggregation operators of trapezoidal intuitionistic fuzzy sets and their application to multi criteria decision making", Neural Computing and Applications, 25(6), pp. 1447-1454 (2014).
54. Ye, J. "Trapezoidal neutrosophic set and its application to multiple attribute decision making", Neural Computing and Applications, 26(5), pp. 1157-1166 (2015).
55. Liang, R.X., Wang, J.Q., and Zhang, H.Y. "A multi-criteria decision-making method based on singlevalued  trapezoidal neutrosophic preference relations with complete weight information", Neural Computing and Applications (2017). DOI: 10.1007/s00521-017- 2925-8.
56. Ji, P., Zhang, H.Y., and Wang, J.Q. "Fuzzy decisionmaking framework for treatment selection based on the combined QUALIFLEX-TODIM method", International Journal of Systems Science, 48(14), pp. 3072- 3086 (2017).
57. Liang, R.X., Wang, J.Q., and Zhang, H.Y. "Evaluation of e-commerce websites: An integrated approach under a single-valued trapezoidal neutrosophic environment", Knowledge-Based Systems, 135, pp. 44-59 (2017).
58. Li, Y., Wang, J., Wang, T.A. "Linguistic neutrosophic multi-criteria group decision-making approach with EDAS method", Arab J Sci Eng, 44, pp. 2737-2749 (2019). DOI: 10.1007/s13369-018-3487-5.
59. Peng, J.J., Wang, J.Q., Hu, J.H., and Tian, C.  Multicriteria decision-making approach based on singlevalued neutrosophic hesitant fuzzy geometric weighted choquet integral heronian mean operator", Journal of Intelligent and Fuzzy Systems, 35(3), pp. 3661-3674 (2018). DOI: 10.3233/IFS-18249.
60. Wang, Y., Wang, J.Q., and Wang, T.L. "Fuzzy stochastic multi-criteria decision-making methods with interval neutrosophic probability based on regret theory", Journal of Intelligent and Fuzzy Systems (2018). DOI: 10.3233/JIFS-17622.
61. Ji, P., Zhang, H.Y., and Wang, J.Q. "Selecting an outsourcing provider based on the combined MABACELECTRE method using single-valued neutrosophic linguistic sets", Computers and Industrial Engineering, 120, pp. 429-441 (2018).
62. Garg, H., Nancy, "Linguistic single-valued neutrosophic prioritized aggregation operators and their applications to multiple-attribute group decisionmaking", Journal of Ambient Intelligence and Humanized Computing, pp. 1-23 (2018). DOI:10.1007/s12652-018-0723-5.
63. Ye, J. "Multi criteria decision-making method using the Dice similarity measure between expected intervals of trapezoidal fuzzy numbers, Journal of Decision Systems, 21(4), pp. 307-317 (2012).
64. Wei, G.W. "Picture fuzzy cross-entropy for multiple attribute decision making problems", J. Bus. Econ. Manag., 17(4), pp. 491-502, (2016).
65. Wu, J. and Liu, Y. "An approach for multiple attribute group decision making problems with interval-valued intuitionistic trapezoidal fuzzy numbers, Computers and Industrial Engineering, 66, pp. 311-324 (2013).
Scientia Iranica
Volume 27, Issue 3
Transactions on Industrial Engineering (E)
May and June 2020
Pages 1655-1673

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