Volume 1 , Issue 1 , PP: 48-54, 2021 | Cite this article as | XML | Html | PDF | Full Length Article
Katy D. Ahmad 1 * , Mikail Bal 2 , Malath Aswad 3
Doi: https://doi.org/10.54216/JNFS.010105
The aim of this paper is to define the concept of kernel subgroup of a fuzzy group and anti-fuzzy group respectively. Also, we prove that these kernels are groups in the ordinary algebraic meaning, as well as presenting many results about fuzzy groups and anti-fuzzy groups.
Fuzzy group, anti-fuzzy group, fuzzy kernel, anti-fuzzy kernel
[1] Zadeh, L., " Fuzzy Sets", Inform. Control, Vol. 8, 1965.
[2] A. ROSENFELD, Fuzzy groups, J. Math. Anal. Appl. 35 ( 1971), 512-517.
[3] P. SIVARAMAKRISHNA DAS, Fuzzy groups and level subgroups, J. Math. Anal. Appl. 84
(1981), 264-269.
[4] T. M. ANTHONY AND H. SHERWOOD, A characterizationo f fuzzy subgroups, F uzzy Sels and
Systems 7 (1982), 297-305.
[5] W. M.Wu, “Normal fuzzy subgroups,” Fuzzy Mathematics, vol.
1, no. 1, pp. 21–30, 1981.
[6] P. Bhattacharya and N.P Mukherjee, “ Fuzzy groups: Some group
theoretical and analogues, “ Inform Sci. 39 (1986),247-268
[7] D.S. Malik, J.N Mordeson and P.S. Nair, “Fuzzy Normal Subgroups in
Fuzzy groups”, J. Korean Math. Soc. 29 (1992), No. 1, pp. 1–8.
[8] D.S. Malik and J.N Mordeson, “ Fuzzy commutative algebra”, World
Scientific Publishing Pvt. Ltd. 1998
[8] Abobala, M., "Neutrosophic Real Inner Product Spaces", NSS, Vol. 43, 2021.
[9] Abobala, M., and Hatip, A., "An Algebraic Approch To Neutrosophic Euclidean Geometry", NSS, Vol. 43, 2021.
[10] Palaniappan, N, Naganathan,S and Arjunan, K “ A study on Intuitionistic L-Fuzzy Subgroups”, Applied Mathematical Sciences, vol. 3 , 2009, no. 53 , 2619-2624
[11] P.K. Sharma , “( α , β ) – Cut of Intuitionistic fuzzy Groups” International
Mathematical Forum ,Vol. 6, 2011 , no. 53 , 2605-2614
[12] Abobala, M., "On The Characterization of Maximal and Minimal Ideals In Several Neutrosophic Rings", NSS , Vol. 45, 2021.
[13] Abobala, M., " A Study Of Nil Ideals and Kothe's Conjecture In Neutrosophic Rings", International Journal of Mathematics and Mathematical Sciences", Hindawi, 2021
[14] Abobala, M., Hatip, A., and Bal, M., " A Review On Recent Advantages In Algebraic Theory Of Neutrosophic Matrices", IJNS, Vol.17, 2021.
[15] Gupta K.c and Sarma B.K., (1999), “nilpotent fuzzy groups” ,fuzzy set and systems , vol.101, pp.167-176 .
[16] Seselja .B. and Tepavcevic A. ,(1996) , “Fuzzy groups and collections of subgroups” , fuzzy sets and systems, vol.83, pp. 85 – 91.
[18] Liu. W.J., (1982), ”Fuzzy invariant subgroups and fuzzy ideals”, fuzzy sets and systems
.vol.8. , pp.133-139 .
[19] Malik . D. s. , Mordeson . J. N. and Nair. P. S., (1992), ” Fuzzy Generators and Fuzzy Direct
Sums of Abelian Groups”, Fuzzy sets and systems, vol.50, pp.193-199
[20] Chandrasekaran, S., and Deepica, N., "Relations between Fuzzy Subgroups and Anti-Fuzzy Subgrous" , IJRIST, Vol.5, 2019