- Volume 33 Issue 3_4
In this paper, we shall introduce the concept of rough antifuzzy subring and prove some theorems in this context. We have, if µ is an anti-fuzzy subring, then µ is a rough anti-fuzzy subring. Also we give some properties of homomorphism and anti-homomorphism on rough anti-fuzzy subring.
rough subring;rough anti-fuzzy subring;ring homomorphism;ring anti-homomorphism
- Neelima C.A and Paul Isaac, Anti-homomorphism on Rough Prime Fuzzy Ideals and Rough Primary Fuzzy Ideals, Ann.Fuzzy Math.Inform., 8 (2014), 549=-559.
- B. Davvaz Roughness in rings, Inform. Sci., 164 (2004), 147–163. https://doi.org/10.1016/j.ins.2003.10.001
- D. Dubois and H. Prade, Rough fuzzy sets and fuzzy rough sets, Int. J. Gen. Syst., 17 (1990), 191–209. https://doi.org/10.1080/03081079008935107
- Nobuaki Kuroki, Rough ideals in semigroups, Inform. Sci., 100 (1997), 139-163. https://doi.org/10.1016/S0020-0255(96)00274-5
- Paul Isaac and Neelima C.A, Anti-homomorphism on Rough Prime Ideals and Rough Primary ideals Advances in Theoretical and Applied Mathematics, 9 (2014), 1–9.
- Osman Kazanci and B. Davvaz, On the structure of rough prime (primary) ideals and rough fuzzy prime (primary) ideals in commutative rings, Inform. Sci., 178 (2008), 1343–1354. https://doi.org/10.1016/j.ins.2007.10.005
- J.N. Mordeson and D.S. Malik, Fuzzy Commutative Algebra, World Scientific (1998), ISBN 981-02-3628-X.
- Z. Pawlak, Rough sets Int. J. Inform. Comput. Sci., 11 (1982), 341-356. https://doi.org/10.1007/BF01001956
- Tariq Shah, Mohammad Saeed, On Fuzzy ideals in rings and Anti-homomorphism, Int. Math. Forum., 7 (2012), 753-759.
- L.A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
- R. Biswas and S. Nanda, Rough groups and rough subgroups, Bull. Polish Acad. Sci. Math., 42 (1994), 251–254.
- Neelima C.A. and Paul Isaac, Rough semi prime ideals and rough bi-ideals in rings, Int. J. Math. Sci. Appl., 4 (2014), 29–36.