Document Type : Research Paper


Universiti Kebangsaan Malaysia,UKM Bangi, Selangor, Malaysia.


In this paper, the (α,β)-level sets where α and β are elements in the interval [0,1] is introduced. Several related properties for (α,β)-cut of intuitionistic fuzzy normed ideals in a normed ring (NR) will be studied and proven. Further, for any two normed rings NR,NR^' with a mapping f:NR → NR^', a relation between the intuitionistic fuzzy normed ideal I of NR and the intuitionistic fuzzy normed ideal f(I) (the image of I) of NR^' will been obtained with the support of their (α,β)-level subsets.


Main Subjects

[1]     Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338–353.
[2]     Rosenfeld, A. (1971). Fuzzy groups. Journal of mathematical analysis and applications, 35(3), 512–517. DOI:10.1016/0022-247X(71)90199-5
[3]     Liu, W. (1982). Fuzzy invariant subgroups and fuzzy ideals. Fuzzy sets and systems, 8(2), 133–139.
[4]     Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy sets and systems, 20(1), 87–96.
[5]     Biswas, R. (1989). Intuitionistic fuzzy subgroups, Mathematical Forum, Vol. Mathematical forum, 10(2), 37–46.
[6]     Hur, K., Kang, H. W., & Song, H. K. (2003). Intuitionistic fuzzy subgroups and subrings. Honam mathematical journal, 25(2), 19–41.
[7]     Banerjee, B., & Basnet, D. (2003). Intuitionistic fuzzy subrings and ideals. Journal of fuzzy mathematics, 11(1), 139–155.
[8]     Abed Alhaleem, N., & Ahmad, A. G. (2020). Intuitionistic fuzzy normed subrings and intuitionistic fuzzy normed ideals. Mathematics, 8(9), 1594.
[9]     Basnet, D. K. (2010). (α, β)-cut of intuitionistic fuzzy ideals. International journal of algebra, 4(27), 22–27.
[10]   Sharma, P. K. (2011). (α,β) – Cut of Intuitionistic Fuzzy Groups. International mathematics forum, 6(53), 2605–2614.
[11]   Adak, A. K., Bhowmik, M., & Pal, M. (2012). Interval cut-set of generalized interval-valued intuitionistic fuzzy sets. International journal of fuzzy system applications (IJFSA), 2(3), 35–50.
[12]   Klir, G., & Yuan, B. (1995). Fuzzy sets and fuzzy logic (Vol. 4). Prentice hall New Jersey.
[13]   M.M. Gupta, J. Q. (1991). Theory of T-norms and fuzzy inference methods. Fuzzy sets and systems, 40(3), 431–450.
[14]   Naimark, M. A. (1959). Normed Rings. Groningen.
[15]   Alhaleem, N. A., & Ahmad, A. G. Bin. (2021). Intuitionistic anti fuzzy normed ideals. Notes on intuitionistic fuzzy sets.
[16]   Alhaleem, N. A., & others. (2021). Intuitionistic fuzzy normed prime and maximal ideals. AIMS mathematics, 6(10), 10565–10581.