Interval valued fuzzy weak bi-ideals of $\Gamma$-near-rings

محورهای موضوعی : Fuzzy, Fuzzy logic, Fuzzy system

V. Chinnadurai ¹ , K. Arulmozhi ² , S. Kadalarasi ³

1 - Department of Mathematics, Annamalai University, Annamalainagar-608 002, India
2 - Department of Mathematics, Annamalai University, Annamalainagar-608 002, India
3 - Department of Mathematics, Annamalai University, Annamalainagar-608 002, India

تاریخ دریافت : 1396/02/21 تاریخ پذیرش : 1396/08/10 تاریخ انتشار : 1396/09/10

کلید واژه: fuzzy weak bi-ideals, interval valued fuzzy weak bi-ideals, homomorphism and anti-homomorphism, $\Gamma$-near-rings,

چکیده مقاله :

In this paper, we introduce the concept of interval valued fuzzy weak bi-ideals of $\Gamma$-near-rings, which is a generalized concept of fuzzy weak bi-ideals of $\Gamma$- near-rings. We also characterize some properties and examples of interval valued fuzzy weak bi-ideals of $\Gamma$-near-rings.

منابع و مأخذ:

[1] G. L. Booth, A note on Γ-near-rings, Stud. Sci. Math. Hung. 23 (1988), 471-475.

[2] Ch. Rao, V. Swaminathan, Anti-homomorphism in fuzzy ideals, International scholarly and scientific research and innovation. 4 (8) (2010), 1211-1214.

[3] V. Chinnadurai, S. Kadalarasi, Fuzzy weak bi-ideals of near-rings, Annals of Fuzzy Mathematics and Informatics. 11 (2016), 799-808.

[4] V. Chinnadurai, K. Arulmozhi, S. Kadalarasi, Interval valued fuzzy ideals of Γ-near-rings, Submitted.

[5] V. Chinnadurai, K. Arulmozhi, S. Kadalarasi, Characterization of fuzzy weak bi-ideals of Γ-near-rings, Submitted.

[6] V. Chinnadurai, K. Arulmozhi, S. Kadalarasi, Interval valued fuzzy bi-ideals of Γ-near-rings, Submitted.

[7] V. Chinnadurai, S. Kadalarasi, interval valued fuzzy quasi-ideals of near-rings, Annals of Fuzzy Mathematics and Informatics. 11 (2016), 621-631.

[8] Y. B. Jun, M. Sapanic, M. A. Ozturk, Fuzzy ideals in gamma near-rings, Tr. J. of Mathematics. 22 (1998), 449-549.

[9] S. D. Kim, H. S. kim, On fuzzy ideals of near-rings, Bull. Korean. Math. Soc. 33 (1996), 593-601.

[10] T. Manikantan, Fuzzy bi-ideals of near-rings, Journal of Fuzzy Mathematics. 17 (3) (2009), 659-671.

[11] M. Murali, k. Rao, B. Venkateswarlu, Anti-fuzzy k-ideals and anti-homomorphism of Γ-semirings, J. International Math. Virtual Institute. 5 (2015), 37-54.

[12] N. Meenakumari, T. Tamizh Chelvam, Fuzzy bi-ideals in gamma near-rings, Journal of Algebra Discrete Structures. 9 (1-2) (2011), 43-52.

[13] Al. Narayanan, T. Manikatan, (∈, ∈ ∨q)−fuzzy subnear-rings and (∈, ∈ ∨q)−fuzzy ideals of near-rings, J. Applied Math. Computing. 27 (2004), 983-998.

[14] G. Pilz, Near-rings, The theory and its applications, North-Holland Publishing Company, Amesterdam, 1983.

[15] Bh. Satyanarayana, Contributions to near-rings theory Doctoral Thesis, Nagarjuna University, 1984.

[16] T. Tamizh Chelvam, N. Meenakumari, Bi-ideals of gamma near-rings, Southeast Bulletion of Mathematics. 27 (2004) 983-998.

[17] N. Thillaigovindan, V. Chinnadurai, Interval valued fuzzy quasi-ideals of semigroups, East Asian Mathematics Journal. 25 (4) (2009), 449-467.

[18] N. Thillaigovindan, V. Chinnadurai, S. Kadalarasi , Interval valued fuzzy ideals of nera-rings, The Journal of Fuzzy Mathematics. 23 (2) (2015), 471-484.

[19] N. Thillaigovindan, V. Chinnadurai, S. Coumaressane, T -fuzzy subsemigroups and T-fuzzy ideals of regular Γ- semigroups, Annals of Fuzzy Mathematics and Informatics. 11 (4) (2016), 669-680.

[20] Y. K. Cho, T. Tamizh Chelvam, S. Jayalakshmi, Weak bi-ideals of near-rings, J. Korean. Soc. Math. Edue. Ser B. Pure Appl. Math. 14 (3) (2007), 153-159.

[21] L. A. Zadeh, Fuzzy sets, Inform and Control. 8 (1965), 338-353.

[22] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning, Inform. Sci. 8 (1975), 199-249.