On accuracy function and distance measures of interval-valued Pythagorean fuzzy sets with application to decision making

Document Type : Article

Authors

1 SRM Institute of Science and Technology, Delhi-NCR Campus, Ghaziabad (UP), India

2 Jaypee University of Information Technology, Waknaghat, Solan(HP), India

3 CMR College of Engineering & Technology, Kandlakoya, Hyderabad (TS), India

Abstract

The notion of interval-valued Pythagorean fuzzy sets permits four important parameters, i.e., membership degree, non-membership degree, and a pair of values strength of commitment and direction of commitment, to a given set to have an interval value in dealing with imprecise information. In the present communication, a new accuracy function is being provided to overcome the shortcomings of the existing score and available accuracy functions for interval-valued Pythagorean fuzzy sets. The validity of the proposed accuracy function has been discussed in detail through the illustrative examples. Further, a new interval-valued Pythagorean fuzzy $p$-distance measure for interval-valued Pythagorean fuzzy numbers has been proposed and used in context with the existing weighted averaging operators. Finally, in view of the proposed accuracy function, distance measure and weighted averaging operators, a numerical example of multi-criteria decision-making problem has been solved to validate the proposed methodology.

Keywords

Main Subjects

References

References:
1. Zadeh, L.A. "Fuzzy sets", Information and Control, 8(3), pp. 338-353 (1965).
2. Atanassov, K.T. "Intuitionistic fuzzy sets", Fuzzy Sets and Systems, 20(1), pp. 87-96 (1986).
3. Garg, H., Agarwal, N., Tripathi, A. "Some improved interactive aggregation operators under interval-valued intuitionistic fuzzy environment and its application to decision making process", Scientia Iranica, 24(5), pp. 2581-2604 (2017).
4. Yager, R.R. "Pythagorean membership grades in multicriteria decision making", IEEE Transaction on Fuzzy Systems, 22, pp. 958-965 (2014).
5. Yager, R.R. and Abbasov, A.M. "Pythagorean membership grades, complex numbers and decision making", International Journal of Intelligent Systems, 28, pp. 436-452 (2013).
6. Zhang, X.L. and Xu, Z.S. "Extension of TOPSIS tomulti-criteria decision making with Pythagorean fuzzy sets", International Journal of Intelligent Systems, 29, pp. 1061-1078 (2014).
7. Peng, X.D. and Yang, Y. "Fundamental properties of interval-valued Pythagorean fuzzy aggregation operators", International Journal of Intelligent Systems, 30, pp. 1-44 (2015).
8. Peng, X.D. "New operations for interval-valued Pythagorean fuzzy set", Scientia Iranica, 26(2), pp. 1049-1076 (2019). DOI: 10.24200/sci.2018.5142.1119.
9. Zhang, X.L. "Multicriteria Pythagorean fuzzy decision analysis: a hierarchical QUALIFLEX approach with the closeness index-based ranking methods", Information Sciences, 330, pp. 104-124 (2016).
10. Chen, T.Y. "Multiple criteria decision analysis under complex uncertainty: A pearson-like correlation -based Pythagorean fuzzy compromise approach", International Journal of Intelligent Systems, pp. 1-38 (2018). https://doi.org/10.1002/int.22045.
11. Tang, X. and Wei, G. "Some generalized Pythagorean 2-tuple linguistic Bonferroni mean operators in multiple attribute decision making", Journal of Algorithms and Computational Technology, 12(4), pp. 387-398 (2018). https://doi.org/10.1177/1748301818791506.
12. Peng, X.D. and Selvachandran, G. "Pythagorean fuzzy set: state of the art and future directions", Artificial Intelligence Review, 52(3), pp. 1873-1927 (2019). DOI:10.1007/s10462-017-9596-9.
13. Peng, X.D. and Yang, Y. "Pythagorean fuzzy choquet integral based MABAC method for multiple attribute group decision making", International Journal of Intelligent Systems, 31(10), pp. 989-1020 (2016).
14. Peng, X.D., Yuan, H.Y., and Yang, Y. "Pythagorean fuzzy information measures and their applications", International Journal of Intelligent Systems, 32(10), pp. 991-1029 (2017).
15. Grzegorzewski, P. "Distance between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric", Fuzzy Sets and Systems, 148, pp. 319-328 (2004).
16. Szmidt, E. and Kacprzyk, J. "Distance between intuitionistic fuzzy sets", Fuzzy Sets and Systems, 114, pp. 505-518 (2000).
17. Xu, Z.S. and Chen, J. "An overview of distance and similarity measures of intuitionistic fuzzy sets", International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 16, pp. 529-555 (2008).
18. Dubois, D. and Prade, H., Fuzzy Sets and Systems: Theory and Applications, New York: Academic Press (1980).
19. Zeng, W.Y. and Guo, P. "Normalized distance, similarity measure, inclusion measure and entropy of intervalvalued fuzzy sets and their relationships", Information Sciences, 178, pp. 1334-1342 (2008).
20. Deqing, L. and Wenyi, Z. "Distance measure of Pythagorean fuzzy sets", International Journal of Intelligent Systems, 33, pp. 348-361 (2018).
21. Liu, Y., Qin, Y., and Han, Y. "Multiple criteria decision making with probabilities in interval-valued Pythagorean fuzzy setting", International Journal of Fuzzy Systems, 20(2), pp. 558-571 (2018).
22. Peng, X.D. and Yang, Y. "Some results for Pythagorean fuzzy sets", International Journal of Intelligent Systems, 30, pp. 1133-1160 (2015).
23. Garg, H. "A novel improved accuracy function for interval valued Pythagorean fuzzy sets and its applications  in the decision-making process", International Journal of Intelligent Systems, 32(12), pp. 1247-1260 (2017).
24. Yager, R.R., Engemann, K.J., and Filev, D.P. "On the concept of immediate probabilities", International Journal of Intelligent Systems, 10, pp. 373-397 (1995).
25. Wei, G.W. and Merigo, J.M. "Methods for strategic decision-making problems with immediate probabilities in intuitionistic fuzzy setting", Scientia Iranica, 19(6), pp. 1936-1946 (2012).
Scientia Iranica
Volume 27, Issue 4
Transactions on Industrial Engineering (E)
July and August 2020
Pages 2127-2139

Files

Share

How to cite

Statistics