Some New Operations on Pythagorean Fuzzy Sets
Keywords:
Intuitionistic fuzzy sets, Pythagorean fuzzy sets, Operations on pythagorean fuzzy setsAbstract
The concept of Pythagorean fuzzy sets (PFSs) was initially developed by Yager in 2013, which provides a novel way to model uncertainty and vagueness with high precision and accuracy compared to Pythagorean fuzzy sets (PFSs).The concept was concretely designed to represent uncertainty and vagueness in mathematical way and to furnish a formalized tool for tackling imprecision to real problems. In this paper, various operations in Pythagorean Fuzzy Sets are discussed. Some theorems are proved for establishing the properties of Pythagorean fuzzy operators with respect to different Pythagorean fuzzy sets.
References
Abdullah, S., Naeem, M., Imran, M. (July 2013). On intuitionistic fuzzy σ-ideals of σ-LA-semigroups. Annals of Fuzzy Mathematics and Informatics. 6(1), 17-31.
A. Abou-Zaid. (1989). On fuzzy subnear-ring. Fuzzy Sets and Systems. 81, 383-393.
Adak, A. K., Bhowmik, M. (2011). Interval cut-set of interval-valued intuitionistic fuzzy sets. African Journal of Mathematics and Computer Sciences. 4(4), 192-200.
Adak, A. K., Bhowmik, M. and Pal, M. Interval cut-set of generalized interval-valued intuitionistic fuzzy sets. International Journal of Fuzzy System Applications. 2 (3) (2012) 35-50.
Adak, A. K., Salokolaei, D. D. (2021). Some Properties Rough Pythagorean Fuzzy Sets. Fuzzy Information and Engineering (IEEE) , 13(4) 420-435.
Adak, A. K.,& Kumar, D. (2022). Some properties of Pythagorean fuzzy ideals of Γ- near rings. Palestine Journal of Mathematics. 11(4), 336-346.
Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems. 20, 87-96.
Biswas, R. (1990). Fuzzy subgroups and anti-fuzzy subroups. Fuzzy Sets and Sys. 35(1), 121-124.
Davvaz, B. (2008). Fuzzy R-subgroups with thresholds of near-rings and implication operators. Soft Computing. 12, 875-879.
Ebrahimnejad, A., Adak, A. K., Jamkhaneh, E.B. (2019). Eigenvalue of Intuitionistic Fuzzy Matrices Over Distributive Lattice. International Journal of Fuzzy System Applications (IJFSA). 8(1), 1-18.
Garg, H. (2016). A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem. J Intell Fuzzy Syst. 31(1), 529-540.
Garg, H. (2016). A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making. Int J Intell Syst. 31(9), 886-920.
Garg, H. (2017). Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for multicriteria decision making process. Int J Intell Syst. 32(6), 597-630.
Jun, Y. B., Kim, K. H., Yon, Y. H. (1999). Intuitionistic fuzzy ideals of near-rings. J. Inst. Math. Comp. Sci. 12 (3), 221-228.
Jun, Y. B. (2002). Interval-valued fuzzy R-subgroups of near-rings. Indian J. pure appl. Math. 33(1), 71-80.
Kim, K. H. Jun, Y. B. (2002). On fuzzy R-subgroups of near-rings. J. Fuzzy Math.. 8, 549-558.
Kuncham, S.P., Bhavanari, S. (2005). Fuzzy prime ideal of a gamma near ring. Soochow Journal of Mathematics. 31 (1), 121-129.
Ma, X., Zhan, J. (2009). On generalized fuzzy R-subgroups of near-rings. International Workshop on Intelligent Systems and Applications. 1724-1727.
Prince Williams, D. R., Latha, K. B., Chandrasekar, E. (March 2013). TG-interval-valued (∈, ∈, ∨q)-fuzzy subgroups, Annals of Fuzzy Mathematics and Informatics. 5(2), 283-300.
Roh, E. H. Roh, Kim, K. H., Lee, J. G., (2006). Intuitionistic Q-Fuzzy Subalgebras of BCK/BCI-Algebras. International Mathematical Forum. 1 (24), 1167-1174.
Yager, R. R., Abbasov, A. M. (2013). Pythagorean membeship grades, complex numbers and decision making. Int J Intell Syst. 28, 436-452.
R. R. Yager, R. R. (2013). Pythagorean fuzzy subsets. In: Proc Joint IFSA World Congress and NAFIPS Annual Meeting. Edmonton, Canada. 57-61.
R. R. Yager, R. R. (2014). Pythagorean membership grades in multicriteria decision making. IEEE Transaction on Fuzzy Systems. 22, 958-965.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338-353.
Zhang, X., Xu, Z.(2014). Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst . 29(12),1061-1078.
Metrics
