(∈,∈ vq_(λ,μ))–Fuzzy (Completely) Regular Subrings

Abstract:

This paper gave the definition of fuzzy (completely) regular subring ,generalized fuzzy (completely) regular subring , fuzzy (completely) regular subring and some properties of them .Baesd on the idea of generalized fuzzy subring,we obtain the equivalent connection between them and discuss some algebraic properties of them .Finally,we give the properties of homomorphic image and homomorphic preimage of fuzzy (completely) regular subring

• Periodical: Advanced Materials Research (Volumes 143-144)
• Pages: 260-264
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.143-144.260
• Online since: October 2010
• Authors: Zu Hua Liao, Shu Cao, Miao Han Hu, Lian Wu
• Keywords: (∈, ∈ V Q_{(λ, μ)})- Fuzzy (Completely) Regular Subring, Fuzzy (Completely) Regular Subring, Generalized Fuzzy (Completely) Regular Subring

References

[1] L. A. Zadeh. Fuzzy sets [J]. Information and Control, 8(1965), p.338.

[2] A. Rosenfeld. Fuzzy groups [J]. Journal of Mathematical Analysis and Applications, 35(1971), p.512.

[3] B. X. Yao. Fuzzy theory on groups and rings. chapter, 3, Sciences Press(2008).

[4] M. AtiMishref. Normal fuzzy subgroups and fuzzy normal series of finite groups [J]. Fuzzy Sets and Systems, 72(1995), p.379.

DOI: 10.1016/0165-0114(94)00288-i

[5] X. H . Yuan, C. Zhang, Y.H. Ren. Generaized fuzzy subgroups and many valued implications [J]. Fuzzy Sets and Systems, 138(2003), p.205.

DOI: 10.1016/s0165-0114(02)00443-8

[6] Z. H. Liao, X. L . Li, H. Q . Sheng , Y Huang , H Gu. About generalized fuzzy subring[J]. Journal of Jiangnan University(natural science), 3(2004): 622.

[7] W.J. Liu. The character of fuzzy ideals and field [J]. Fuzzy Mathematics, 1(1981): 101.

[8] S . K . Bhakat, P . Das. On the Defenition of a Fuzzy Subgroup[J]. Fuzzy Sets and Systems, 51(1992)p.235.

DOI: 10.1016/0165-0114(92)90196-b

[9] S . K . Bhakat, P . Das. Fuzzy subrings and ideals redefined[J]. Fuzzy Sets and Systems, 81(1996), p.383.

DOI: 10.1016/0165-0114(95)00202-2

[10] B. J. Zhao, H. G . Chi. Fuzzy subrings and ideals redifind[J]. Journal of Liaoning normal university (natural science), 24(2001), p.340.

[11] Z.Y. Guo, Z. H. Liao. ( )( ), q λµ' , ∈ ∈ ∨ − Fuzzy subgroups[C]. In: Lhasa, Tibet. The sixth Internation-al Conference on Information and ManagementSciences. 2007, p.570.

[12] J . Du, Z. H. Liao. ( )( ), q λµ∈ ∈∨ − Generalized fuzzy ideal of BCH-Algebra[C]. In: Hai Kou, Hai Nan. The Fourth International Conference on Fuzzy Systems and Knowledge Discovery, 2007, p.294.

DOI: 10.1109/fskd.2007.1

[13] Z. H. Liao, H . Gu( , ( ), q λµ∈ ∈∨ )-fuzzy normal subgroup[J]. Fuzzy Systems and Mathe matics, 20(2006), p.38.

[14] Z. H . Liao, M . Chen. ( ( , ), q λµ∈ ∈∨ )-fuzzy subsemigroup and ( , ∈ ∈∨ ( , )q λµ -fuzzycompletely regular subsemigroup [J]. Journal of Jiangnan University(natural science), 8(2009), p.242.

[15] Z. H. Liao, Y .X. Chen, J . H . Lu, H . Gu. Generalized fuzzy subsemigroup and Generalized fuzzy completely regular subsemigroup [J]. Fuzzy System and Mathematics, 18(2004), p.81.