An Overview of Pythagorean Fuzzy Sets and Their Distance and Similarity Criteria

Document Type : Original Article

Author

20.1001.1.27174409.1399.3.1.6.1/DOR

Abstract

Pythagorean fuzzy arrays, an extension of fuzzy arrays, are a new tool for dealing with ambiguity and are used in a variety of contexts. In this article, the concepts related to these collections are reviewed and due to the great importance of distance and similarity criteria in many fields such as medical diagnosis, pattern recognition, etc., the distance and similarity criteria introduced for these collections are examined.

Keywords


[1] Atanassov, K.T. (1986) Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87-96.
 
[2] Chachi, J. and Taheri, S.M. (2013) A unified approach to similarity measures between intuitionistic fuzzy sets. International Journal of Intelligent Systems, 28, 669-685.
 
[3] Dubois, D. and Prade H. (1983) On distances between fuzzy points and their use for plausible reasoning. Proc. Int. Conf. on Systems, Man and Cybernetics, 300-303.
 
[4] Khan, M.S.A., Abdullah, S., Ali, A. and Amin, F. (2019) An extension of VIKOR method for multi-attribute decision-making under Pythagorean hesitant fuzzy setting. Granular Computing, 4, 421-434.
 
[5] Pérez-Domínguez, L., Rodríguez-Picón, L.A., Alvarado-Iniesta, A., Luviano Cruz, D. and Xu, Z. (2018) MOORA under Pythagorean fuzzy set for multiple criteria decision making. Complexity, 2018.
 
[6] Peng, X. and Yang, Y. (2016) Fundamental properties of interval-valued Pythagorean fuzzy aggregation operators. International Journal of Intelligent Systems, 31, 444-487.
 
[7] Peng, X., Yuan, H. and Yang, Y. (2017) Pythagorean fuzzy information measures and their applications. International Journal of Intelligent Systems, 32, 991-1029.
 
[8] Rahman, K., Abdullah, S., Shakeel, M., Khan, M.S.A. and Ullah, M. (2017) Interval-valued Pythagorean fuzzy geometric aggregation operators and their application to group decision making problem. Cogent Mathematics & Statistics, 4, 1338638.
 
[9] Szmidt, E. (2014) Distances and similarities in intuitionistic fuzzy sets, Springer.
 
[10] Szmidt, E. and Kacprzyk, J. (2000) Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems, 114, 505-518.
 
[11] Xuecheng, L. (1992) Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets and Systems, 52, 305-318.
 
[12] Yager, R.R. (2013) Pythagorean fuzzy subsets. 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), Edmonton, Canada, 57-61.
 
[13] Yager, R.R. (2013) Pythagorean membership grades in multicriteria decision making. IEEE Transactions on Fuzzy Systems, 22, 958-965.
 
[14] Zadeh, L.A. (1965) Fuzzy sets. Information and Control, 8, 338-353.
 
[15] Zhang, X. and Xu, Z. (2014) Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. International Journal of Intelligent Systems, 29, 1061-1078.