New operations for interval-valued Pythagorean fuzzy set

Document Type : Article

Author

School of Information Science and Engineering, Shaoguan University, Shaoguan, People's Republic of China.

Abstract

Interval-valued Pythagorean fuzzy set (IVPFS), originally proposed by Peng and Yang, is a novel tool to deal with vagueness and incertitude. As a generalized set, IVPFS has close
relationship with interval-valued intuitionistic fuzzy set (IVIFS). IVPFS can be reduced to IVIFS satisfying the
condition $\mu^++\nu^+ \leq 1$. However, the related operations of IVPFS do not take different conditions
into consideration. In this paper, we initiate some new interval-valued Pythagorean fuzzy operators ($\diamondsuit, \Box, \spadesuit, \clubsuit, \maltese, \rightarrow, \$ $) and discuss their properties in relation with some existing operators $(\cup, \cap, \oplus, \otimes)$ in detail. It will promote the development of interval-valued Pythagorean fuzzy operators. Later, we propose an algorithm to deal with multi-attribute decision making (MADM) problem based on proposed $\spadesuit$ operator. Finally, the effectiveness and feasibility of approach is
demonstrated by mine emergency decision making example.

Keywords

Main Subjects

References

References:
1. Atanassov, K.T. "Intuitionistic fuzzy sets", Fuzzy Sets Syst., 20(1), pp. 87-96 (1986).
2. Zadeh, L.A. "Fuzzy sets", Inform. Control., 8(3), pp. 338-356 (1965).
3. Yager, R.R. "Pythagorean fuzzy subsets", Proc. Joint IFSA World Congress NAFIPS Annual Meet., 1, Edmonton, Canada, pp. 57-61 (2013).
4. Yager, R.R. and Abbasov, A.M. "Pythagorean membership grades, complex numbers, and decision making", Int. J. Intell. Syst., 28(5), pp. 436-452 (2014).
5. Zhang, X.L. and Xu, Z.S. "Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets", Int. J. Intell. Syst., 29(12), pp. 1061-1078 (2014).
6. Yang, Y., Ding, H., Chen, Z.S., and Li Y.L. "A Note on extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets", Int. J. Intell. Syst., 31(1), pp. 68-72 (2015).
7. Yager, R.R. "Pythagorean membership grades in multicriteria decision making", IEEE Trans. Fuzzy Syst., 22(4), pp. 958-965 (2014).
8. Peng, X.D. and Yang, Y. "Some results for Pythagorean fuzzy sets", Int. J. Intell. Syst., 30(11), pp. 1133-1160 (2015).
9. Garg, H. "Some methods for strategic decision-making problems with immediate probabilities in Pythagorean fuzzy environment", Int. J. Intell. Syst., 33(4), pp. 687-712 (2018).
10. Zhang, X.L. "Multicriteria Pythagorean fuzzy decision analysis: A hierarchical QUALIFLEX approach with the closeness index-based ranking methods", Inform. Sci., 330, pp. 104-124 (2016).
11. Peng, X.D. and Dai, J.G. "Approaches to Pythagorean fuzzy stochastic multi-criteria decision making based on prospect theory and regret theory with new distance measure and score function", Int. J. Intell. Syst., 32(11), pp. 991-1029 (2017).
12. Ren, P.J., Xu, Z.S., and Gou, X.J. "Pythagorean fuzzy TODIM approach to multi-criteria decision making", Appl. Soft Comput., 42, pp. 246-259 (2016).
13. Peng, X.D. and Yang, Y. "Pythagorean fuzzy choquet integral based MABAC method for multiple attribute group decision making", Int. J. Intell. Syst., 31(10), pp. 989-1020 (2016).
14. Garg, H. "A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making", Int. J. Intell. Syst., 31(9), pp. 886-920 (2016).
15. Garg, H. "Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and tconorm for multicriteria decision-making process", Int. J. Intell. Syst., 32(6), pp. 597-630 (2017).
16. Zeng, S.Z., Chen, J.P., and Li, X.S. "A hybrid method for Pythagorean fuzzy multiple-criteria decision making", Int. J. Inf. Tech. Decis., 15(2), pp. 403-422 (2016).
17. Liang, W., Zhang, X.L., and Liu, M.F. "The maximizing deviation method based on interval-valued Pythagorean fuzzy weighted aggregating operator for multiple criteria group decision analysis", Discrete Dyn. Nat. Soc., 2015(1), pp. 1-15 (2015).
18. Garg, H. "Confidence levels based Pythagorean fuzzy aggregation operators and its application to decisionmaking process", Comput. Math. Organ. Theory, 23(4), pp. 546-571 (2017).
19. Ma, Z.M. and Xu, Z.S. "Symmetric Pythagorean fuzzy weighted geometric/averaging operators and their application in multicriteria decision-making problems", Int. J. Intell. Syst., 31(12), pp. 1198-1219 (2016).
20. Zeng, S.Z. "Pythagorean fuzzy multiattribute group decision making with probabilistic information and OWA approach", Int. J. Intell. Syst., 32(11), pp. 1136- 1150 (2017).
21. Peng, X.D. and Yang, Y. "Fundamental properties of interval-valued Pythagorean fuzzy aggregation operators", Int. J. Intell. Syst., 31(5), pp. 444-487 (2016).
22. Wei, G.W. and Lu, M. "Pythagorean fuzzy maclaurin symmetric mean operators in multiple attribute decision making", Int. J. Intell. Syst., (2017). URL http://onlinelibrary.wiley.com/doi/10.1002/int.21911 /full.
23. Garg, H. "A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decisionmaking processes", Int. J. Intell. Syst., 31(12), pp. 1234-1252 (2016).
24. Peng, X.D., Yuan, H.Y., and Yang, Y. "Pythagorean fuzzy information measures and their applications", Int. J. Intell. Syst., 32(10), pp. 991-1029 (2017).
25. Zhang, X.L. "A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making", Int. J. Intell. Syst., 31(6), pp. 593- 611 (2016).
26. Peng, X.D., Yang, Y., Song, J.P., and Jiang, Y. "Pythagorean fuzzy soft set and its application", Comput. Eng., 41(7), pp. 224-229 (2015).
27. Peng, X.D. and Yang, Y. "Multiple attribute group decision making methods based on Pythagorean fuzzy linguistic set", Comput. Eng. Appl., 52(23), pp. 50-54 (2016).
28. Liu, Z., Liu, P., Liu, W., and Pang, J. "Pythagorean uncertain linguistic partitioned Bonferroni mean operators and their application in multi-attribute decision making", J. Intell. Fuzzy Syst., 32(3), pp. 2779-2790 (2017).
29. Zhang, C., Li, D.Y., and Ren, R. "Pythagorean fuzzy multigranulation rough set over two universes and its applications in merger and acquisition", Int. J. Intell. Syst., 31(9), pp. 921-943 (2016).
30. Liang, D.C. and Xu, Z.S. "The new extension of TOPSIS method for multiple criteria decision making with hesitant Pythagorean fuzzy sets", Appl. Soft Comput., 60, pp. 167-179 (2017).
31. Du, Y., Hou, F., Zafar, W., Yu, Q., and Zhai, Y. "A novel method for multiattribute decision making with interval-valued Pythagorean fuzzy linguistic information", Int. J. Intell. Syst., 32(10), pp. 1085-1112 (2017).
32. Garg, H. "A novel accuracy function under intervalvalued Pythagorean fuzzy environment for solving multicriteria decision making problem", J. Intell. Fuzzy Syst., 31(1), pp. 529-540 (2016).
33. Gou, X.J., Xu, Z.S., and Ren, P.J. "The properties of continuous Pythagorean fuzzy information", Int. J. Intell. Syst., 31(5), pp. 401-424 (2016).
34. Peng, X.D. and Yuan, H.Y. "Fundamental properties of Pythagorean fuzzy aggregation operators", Fund. Inform., 147(4), pp. 415-446 (2016).
35. Peng, X.D. and Selvachandran, G. "Pythagorean fuzzy set state of the art and future directions", Artif. Intell. Rev. (2017).
URL https://link.springer.com/article/10.1007/s10462- 017-9596-9.
36. Garg, H. "A novel improved accuracy function for interval valued Pythagorean fuzzy sets and its applications in decision making process", Int. J. Intell. Syst., 32(12), pp. 1247-1260 (2017).
37. Rahman, K., Abdullah, S., Shakeel, M., Khan, M., and Ullah, M. "Interval-valued Pythagorean fuzzy geometric aggregation operators and their application to group decision making problem", Cogent. Math., 4, pp. 1-20 (2017).
38. Garg, H. "A new improved score function of an interval-valued Pythagorean fuzzy set based TOPSIS method", Int. J. Uncertainty Quantif., 7(5), pp. 463- 474 (2017).
39. Chen, T.Y. "An interval-Valued Pythagorean fuzzy outranking method with a closeness-based assignment model for multiple criteria decision making", Int. J. Intell. Syst., 33(1), pp. 126-168 (2018).
40. Atanassov, K.T. and Gargov, G. "Interval-valued intuitionistic fuzzy sets", Fuzzy Sets Syst., 31(3), pp. 343-349 (1989).
41. Xu, Z.S. "Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making", Control Decis., 22(2), pp. 215- 219 (2007).
42. Hao, Z.N., Xu, Z.S., Zhao, H., and Fujita, H. "A dynamic weight determination approach based on the intuitionistic fuzzy Bayesian network and its application to emergency decision making", IEEE Trans. Fuzzy Syst., 26(4), pp. 1893-1907 (2018) .URL http://ieeexplore.ieee.org/abstract/document/8047330/.
43. Alcantud, J.C.R. and Mathew, T.J. "Separable fuzzy soft sets and decision making with positive and negative attributes", Appl. Soft Comput., 59, pp. 586-595 (2017).
44. Zhan, J.M, Liu, Q., and Tutut, H. "A novel soft rough set soft rough hemirings and its multicriteria group decision making", Appl. Soft Comput., 54, pp. 393-402 (2017).
45. Wang, J., Wang, J.Q., and Zhang, H.Y. "A likelihoodbased TODIM approach based on multi-hesitant fuzzy linguistic information for evaluation in logistics outsourcing", Comput. Ind. Eng., 99, pp. 287-299 (2016).
46. Shariati, S., Abedi, M., Saedi, A., Yazdani-Chamzini, A., Tamosaitien_e, J., Saparauskas, J., and Stupak, S. "Critical factors of the application of nanotechnology in construction industry by using ANP technique under fuzzy intuitionistic environment", J. Civ. Eng. Manag., 23(7), pp. 914-925 (2017).
47. Peng, X.D. "Hesitant trapezoidal fuzzy aggregation operators based on Archimedean t-norm and t-conorm and their application in MADM with completely unknown weight information", Int. J. Uncertainty Quantif., 7(6), pp. 475-510 (2017).
48. Alcantud, J.C.R. "A novel algorithm for fuzzy soft set based decision making from multiobserver input parameter data set", Inform. Fusion, 29, pp. 142-148 (2016).
49. Garg, H. "Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm and their application to decision making", Comput. Ind. Eng., 101, pp. 53-69 (2016).
50. Garg, H. "A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems", Appl. Soft Comput., 38, pp. 989-999 (2016).
51. Garg, H. "Distance and similarity measures for intuitionistic multiplicative preference relation and its applications", Int. J. Uncertainty Quantif., 7(2), pp. 117-133 (2017).
52. Peng, X.D. and Yang, Y. "Algorithms for intervalvalued fuzzy soft sets in stochastic multi-criteria decision making based on regret theory and prospect theory with combined weight", Appl. Soft Comput., 54, pp. 415-430 (2017).
53. Peng, X.D. and Liu, C. "Algorithms for neutrosophic soft decision making based on EDAS, new similarity measure and level soft set", J. Intell. Fuzzy Syst., 32(1), pp. 955-968 (2017).
54. Zhan, J.M., Ali, M., and Mehmood, N. "On a novel uncertain soft set model Z-soft fuzzy rough set model and corresponding decision making methods", Appl. Soft Comput., 56, pp. 446-457 (2017).
55. Ma, X.L., Liu, Q., and Zhan, J.M. "A survey of decision making methods based on certain hybrid soft set models", Artif. Intell. Rev., 47(4), pp. 507-530 (2017).
56. Garg, H. and Kumar, K. "A novel correlation coefficient of intuitionistic fuzzy sets based on the connection number of set pair analysis and its application", Sci. Iran., 25(4), pp. 2373-2388 (2018). URL http://scientiairanica.sharif.edu/article 4454.html.
57. 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", Sci. Iran., 24(5), pp. 2581-2604 (2017).
Scientia Iranica
Volume 26, Issue 2 - Serial Number 2
Transactions on Industrial Engineering (E)
March and April 2019
Pages 1049-1076

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History

  • Receive Date: 06 September 2017
  • Revise Date: 11 November 2017
  • Accept Date: 27 January 2018

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