Geodesic
T-rough Semiprime Ideals on Commutative Rings
Hosseini, S. B.1
1 Department of Mathematics, Islamic Azad University, Sari Branch, Sari, Iran
Journal of nonlinear sciences and its applications, Tome 4 (2011) no. 4, p. 270-280.

Voir la notice de l'article provenant de la source International Scientific Research Publications

Rough sets were originally proposed in the presence of an equivalence relation. An equivalence relation is sometimes difficult to be obtained in rearward problems due to the vagueness and incompleteness of human knowledge. The purpose of this paper is to introduce and discuss the concept of T-rough semiprime ideal, T-rough fuzzy semiprime ideal and T-rough quotient ideal in a commutative ring which are a generalization of rough set and approximation theory. We compare relation between a rough ideal and a T-rough ideal and prove some theorems.
DOI : 10.22436/jnsa.004.04.05
Classification : 03B52, 03F55, 06D72
Keywords: approximation space, rough ideal, semiprime ideal, T-rough set, set-valued homomorphism, T-rough semiprime ideal, T-rough fuzzy ideal, commutative ring.

Hosseini, S. B. 1

1 Department of Mathematics, Islamic Azad University, Sari Branch, Sari, Iran 
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Hosseini, S. B. T-rough Semiprime Ideals on Commutative Rings. Journal of nonlinear sciences and its applications, Tome 4 (2011) no. 4, p. 270-280. doi : 10.22436/jnsa.004.04.05. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.004.04.05/

[1] Biswas, R. On rough sets and fuzzy rough sets , Bull. Pol.Acad. Sci. Math. , Volume 42 (1994), pp. 345-349

[2] Biswas, R. On rough fuzzy sets, Bull. Pol. Acad. Sci. Math., Volume 42 (1994), pp. 352-355

[3] Biswas, R.; S. Nanda Rough groups and rough subgroups, Bull. Polish Acad. Sci. Math , Volume 42 (1994), pp. 251-254

[4] Bonikowaski, Z. Algebraic structures of rough sets, in: W.P. Ziarko (Ed.), Rough Sets, Fuzzy Sets and Knowledge Discovery, Springer-Verlag, Berlin (1995), pp. 242-247

[5] Davvaz, B. A short note on algebraic T-rough sets, Information Sciences , Volume 178 (2008), pp. 3247-3252

[6] Davvaz, B. Roughness in rings, Inform. Sci. , Volume 164 (2004), pp. 147-163

[7] Dubois, D.; Prade, H. Rough fuzzy sets and fuzzy rough sets, Int. J. General Syst., Volume 17 (2-3) (1990), pp. 191-209

[8] Dubois, D.; Prade, H. Two fold fuzzy sets and rough sets-some issues in knowledge representation, Fuzzy Sets Syst. , Volume 23 (1987), pp. 3-18

[9] Hosseini, S. B.; Jafarzadeh, N.; Gholami, A. T-rough Ideal and T-rough Fuzzy Ideal in a Semigroup, Advanced Materials Research , Volume 433-440 (2012), pp. 4915-4919

[10] Hosseini, S. B.; Jafarzadeh, N.; Gholami, A. Some Results on T-rough (prime, primary) Ideal and T-rough Fuzzy (prime, primary) Ideal on Commutative Rings, Int. J. Contemp. Math. Sciences, Volume 7 (2012), pp. 337-350

[11] Hosseini, S. B.; Jafarzadeh, N.; Gholami, A. Some Results on T-rough (prime, primary) Ideal and T-rough Fuzzy (prime, primary) Ideal on Commutative Rings, Int. J. Contemp. Math. Sciences, Volume 7 (2012), pp. 337-350

[12] Iwinski, T. Algebraic approach to rough sets, Bull. PolishAcad. Sci. Math. , Volume 35 (1987), pp. 673-683

[13] Osman Kazanci; Sultan Yamak; Davvaz, B. On the structure of rough prime (primary) ideals and rough fuzzy prime (primary) ideals in commutative rings, Information Sciences, Volume 178 (2008), pp. 2349-2359

[14] N. Kuroki Rough ideals in semigroups, Inform. Sci. , Volume 100 (1997), pp. 139-163

[15] Nakamura, A. Fuzzy rough sets, Note on Multiple-valued Logic in Japan, Volume 9 (8) (1988), pp. 1-8

[16] Nanda, S. Fuzzy rough sets, Fuzzy Sets and Systems, Volume 45 (1992), pp. 157-160

[17] Pawlak, Z. Rough sets basic notions , ICS PAS Rep. 436 , , 1981

[18] Pawlak, Z. Rough sets , Int. J. Inform. Comput. Sci. , Volume 11 (1982), pp. 341-356

[19] Z. Pawlak Rough sets power set hierarchy, ICS PAS Rep.470 , , 1982

[20] Pawlak, Z. Rough sets algebraic and topological approach, ICS PAS Rep. 482 , , 1982

[21] Z. Pawlak Rough sets and fuzzy sets, Fuzzy Sets and Systems, Volume 17 (1985), pp. 99-102

[22] Pawlak, Z. Rough sets, Theoretical Aspects of Reasoning about Data , Kluwer Academic Publishers, Dordrecht, 1991

[23] Pawlak, Z. Rough Sets - Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishing, Dordrecht, 1991

[24] Pawlak, Z. Some remarks on rough sets, Bull. Pol. Acad.Tech. , , 1985

[25] Pawlak, Z.; Skowron, A. Rough sets and Boolean reasoning, Information Sciences, Volume 177 (2007), pp. 41-73

[26] Pawlak, Z.; Skowron, A. Rough sets: some extensions, Information Sciences, Volume 177 (2007), pp. 28-40

[27] Pawlak, Z.; Skowron, A. Rudiments of rough sets, Information Sciences, Volume 177 (2007), pp. 3-27

[28] Rosenfeild, A. Fuzzy Groups, Journal of Mathematical Analysis and Appl ication, Volume 35 (1971), pp. 512-517

[29] Xiao, Qi-Mei; Zhang, Zhen-Liang Rough prime ideals and rough fuzzy prime ideals in semi- groups, Information Sciences, Volume 176 (2006), pp. 725-733

[30] Yamak, S.; Kazanci, O.; Davvaz, B. Generalized lower and upper approximations in a ring, Information Sciences , Volume 180 (2010), pp. 1759-1768

[31] L. A. Zadeh Fuzzy sets , Inform. Control , Volume 8 (1965), pp. 338-353

[32] Zhang, W.; Wu, W. Theory and Method of Roughness, Science Press, Beijing, 2001

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