Pythagorean Fuzzy Strong Bi-ideal and Direct Product of Pythagorean Fuzzy Ideals in Near Ring




Strong bi-ideal, Near ring, Pythagorean fuzzy set, Direct product


In this paper, we introduce the notions of Pythagorean fuzzy strong bi-ideals and Direct Product Pythagorean fuzzy ideals in near ring. Also, study some of their related properties in detail.


Download data is not yet available.

Author Biography

J. Marynirmala, Department of Mathematics, Annamalai University, Annamalai Nagar, Tamil Nadu, India




S. Abou-Zaid, On fuzzy subnear-rings and ideals, Fuzzy Sets and Systems 44 (1991), 139 – 146, DOI: 10.1016/0165-0114(91)90039-S.

K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), 87 – 96, DOI: 10.1016/S0165-0114(86)80034-3.

V. Chinnadurai and S. Kadalarasi, Direct product of fuzzy ideals of near-rings, Annals of Fuzzy Mathematics and Informatics 12(2) (2016), 193 – 204, URL:

S. U. Devi, S. Jayalakshmi and T. T. Chelvam, Intuitionistic fuzzy strong bi-ideals of near-rings, International Journal of Current Research 9(3) (2017), 48353 – 48359.

T. K. Dutta and B. K. Biswas, Fuzzy ideal of a near-ring, Bulletin of the Calcutta Mathematical Society 89(6) (1997), 447 – 456.

K. H. Kim, On fuzzy R-subgroup of near-rings, Journal of Fuzzy Mathematics 8 (2000), 549 – 558.

S. D. Kim and H. S. Kim, On fuzzy ideals of near-rings, Bulletin of the Korean Mathematical Society 33(4) (1996), 593 – 601.

K. H. Kim and Y. B. Jun, Normal fuzzy R-subgroups in near-rings, Fuzzy Sets and Systems 121 (2016), 341 – 345, DOI: 10.1016/S0165-0114(00)00022-1.

K. H. Kim and Y. B. Jun, On fuzzy R-subgroups of near-rings, Journal of Fuzzy Mathematics 11(3) (2003), 567 – 580.

W.-J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems 8 (1982), 133 – 139, DOI: 10.1016/0165-0114(82)90003-3.

A. L. Narayanan, Fuzzy ideals on strongly regular near-rings, Journal of Indian Mathematical Society 69(1-4) (2002), 193 – 199.

A. L. Narayanan and T. Manikantan, (2,2 _q)-fuzzy subnear-rings and (2,2 _q)-fuzzy ideals of near-rings, Journal of Applied Mathematics and Computing 18(1-2) (2005), 419 – 430, DOI: 10.1007/BF02936584.

A. Rosenfeld, Fuzzy groups, Journal of Mathematical Analysis and Applications 35 (1971), 512 – 517, DOI: 10.1016/0022-247X(71)90199-5.

H. K. Saikia and L. K. Barthakur, On fuzzy N-subgroups and fuzzy ideals of near-rings and near-ring groups, Journal of Fuzzy Mathematics 11(3) (2003), 567 – 580.

R. R. Yager, Pythagorean fuzzy subsets, in: Proceedings of the 2013 Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada (2013), 57 – 61, DOI: 10.1109/IFSANAFIPS.2013.6608375.

L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338 – 353, DOI: 10.1016/S0019-9958(65)90241-X.




How to Cite

Marynirmala, J., & Sivakumar, D. (2021). Pythagorean Fuzzy Strong Bi-ideal and Direct Product of Pythagorean Fuzzy Ideals in Near Ring. Communications in Mathematics and Applications, 12(4), 1079–1100.



Research Article