Acknowledgement
The authors wish to thank the anonymous reviewers for their valuable suggestions.
References
- S. Abou-Zaid, On Fuzzy subnear-rings and ideals, Fuzzy Sets and Systems 44 (1991), 139-146.
- M.I. Ali, F. Feng and M. Shabir, A note on (∈, ∈ ∨q)-fuzzy equivalence relations and indistinguishability operations, Hacettape Journal of Mathematics and Statistics 40 (2011), 383-400.
- S.K. Bhakat, (∈ ∨q)-level subset, Fuzzy Sets and Systems 103 (1999), 529-533.
- S.K. Bhakat and P. Das, On the definition of a fuzzy subgroup, Fuzzy Sets and Systems 51 (1992), 235-241.
- S.K. Bhakat and P. Das, (∈, ∈ ∨q)-fuzzy subgroup, Fuzzy Sets and Systems 80 (1996), 359-368.
- S.K. Bhakat and P. Das, Fuzzy subrings and ideals redefined, Fuzzy Sets and Systems 81 (1996), 383-393.
- P. Bhattacharya and N.P Mukherjee, Fuzzy relations and fuzzy groups, Information Sciences 36 (1985), 267-282.
- M. Chakraborty and S. Das, On fuzzy equivalence I, Fuzzy sets and Systems 11 (1983), 185-193.
- M. Chakraborty and S. Das, On fuzzy equivalence II, Fuzzy sets and Systems 12 (1983), 299-307.
- P.S. Das, Fuzzy groups and level subgroups, Journal of Mathematical Analysis and Applications 84(1) (1981), 264-269.
- K.C. Gupta and R.K. Gupta, Fuzzy equivalent relation redefined, Fuzzy Sets and Systems 79 (1996), 227-23.
- K.C. Gupta and T.P. Singh, Fuzzy G-congruences on a groupoid, Fuzzy Sets and Systems 93 (1998), 211-222.
- K.C. Gupta and T.P. Singh, Fuzzy G-equivalences and G-congruences on a groupoid under semibalanced maps, Fuzzy Sets and Systems 108 (1999), 111-116.
- J.P. Kim and D.R. Bae, Fuzzy congruence in groups, Fuzzy Sets System 85 (1997), 115-120.
- N. Kuroki, Fuzzy Congruences and Fuzzy Normal Subgroups, Information Sciences 60 (1992), 247-259.
- W.J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy sets and Systems 8 (1982), 133-139.
- Liu, Yong Lin, Jie Meng, and Xiao Long Xin, Quotient rings induced via fuzzy ideals, Korean Journal of Computational and Applied Mathematics 8 (2001), 631-643.
- B.B. Makamba and V. Murali, Normality and Congruence in Fuzzy Subgroups, Information Sciences 59 (1992), 121-129.
- P.P. Ming and L.Y. Ming, Fuzzy topology I, Neighborhood structure of a fuzzy point and Moore-Smith convergence, Journal of Mathematical Analysis and Applications 76 (1980), 571-599.
- N.P. Mukherjee, and P. Bhattacharya, Fuzzy normal sub-groups and fuzzy cosets, Information Sciences 34 (1984), 225-239.
- V. Murali, Fuzzy Equivalence Relations, Fuzzy Sets and Systems 30 (1989), 155-163.
- V. Murali, Fuzzy Congruence Relations, Fuzzy Sets and Systems 41 (1991), 359-369.
- Nemitz and C. William, Fuzzy relations and fuzzy functions, Fuzzy Sets and Systems 19 (1986), 177-191.
- N. Pradipkumar and O. Ratanabala Devi, (∈, ∈ ∨q)-fuzzy congruences on Groups, Bulletin Calcutta Mathematical Society 114 (2022), 597-616.
- A. Rosenfeld, Fuzzy groups, Journal of Mathematical Analysis and Applications 35 (1971), 512-517.
- M.A. Samhan, Fuzzy congruence on semigroups, Information Sciences 74 (1993), 165-175.
- M.A. Samhan and T.G.M. Ahsanullah, Fuzzy congruence on groups and rings, International Journal of Mathematics and Mathematical Sciences 17 (1994), 469-474.
- Y.O. Sung and B.G. Son, Notes of fuzzy congruences, Far East J. Math. Sci. 100 (2016), 385-396.
- L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353.
- L.A. Zadeh, Similarity relations and fuzzy ordering, Information Sciences 3 (1971), 177-200.
- Zhou, Xiaowu, Dajing Xiang, and Jianming Zhan, Quotient rings via fuzzy congruence relations, Italian Journal of Pure and Applied Mathematics 33 (2014), 411-424.