(λ,μ)-fuzzy Subrings and (λ,μ)-fuzzy Quotient Subrings with Operators

In this paper, we extend the fuzzy subrings with operators to the (λ, μ)-fuzzy subrings with operators. And the concepts of the (λ, μ)-fuzzy subring with operators and (λ, μ)-fuzzy quotient ring with operators are gived, while their elementary properties are discussed.

• Shaoquan Sun
• Chunxiang Liu

• Fuzzy subring with operators
• (λ
• μ)-fuzzy subring with operators
• (λ
• μ)-fuzzy quotient ring with operators.

[1] Liu W J. Fuzzy invariant subgroups and Fuzzy ideals (J). Fuzzy Sets and Systems, 1982, 8: 133-139.
[2] Yin Y T. W. Fuzzy ideals and fuzzy quotient rings (J). Fuzzy Math. 1985, 4: 19-26.
[3] Kuraoka T, Nobuaki. On fuzzy quotient-rings included by fuzzy ideals [J]. Fuzzy Sets and Systems, 1992, 47: 381-386.
[4] Shaoquan Sun, Wenxiang Gu. Fuzzy subrings with operators and Fuzzy ideals with operators. Fuzzy Sets and Systems, 2005, 19(2):
[5] Yao B. (λ, μ)-fuzzy subrings normal and (λ, μ)-fuzzy ideals. The Journal of Fuzzy Mathematics. 2007, 15(4): 981-987.
[6] M. Jiang, X.L. Xin, “(λ, μ) Intuitionistic Fuzzy Subrings (Ideals),” Fuzzy Systems and Mathematics, vol. 27, pp. 1-8, 2013.
[7] Quanyan Xiong. Modern algebra (M). Shanghai: Shanghai Scientific and Technical Publishers, 1963.
[8] Yao B. Fuzzy theory of groups and rings (M). Beijing: Science Press, 2008.