T-rough Fuzzy Subgroups of Groups

Volume 12, Issue 3, pp 186-195 http://dx.doi.org/10.22436/jmcs.012.03.02

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Authors

Eshagh Hosseinpour - Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran.

Abstract

The rough set theory was introduced by Pawlak in 1982. It was proposed for presentation equivalence relations. But the concept of fuzzy set was introduced by Zadeh in 1965. In this paper,the concepts of the rough sets,T-rough sets,T-rough fuzzy sets, T-rough fuzzy subgroups, T-rough fuzzy ideals, and set-valued homomorphism of groups will be given. A necessery and sufficient condition for a fuzzy subgroup(ideal) and fuzzy prime ideal of a group under a set-valued homomorphism to be a T-rough fuzzy subgroup(ideal) and T-rough fuzzy prime ideal is stated. The purpose of this paper is to introduce and discuss the concept of T-rough fuzzy groups of groups that those have been proved in several papers. Also, we proved that intersection two fuzzy subgroups(ideals) of a set under a set-valued homomorphism is a T-rough fuzzy subgroup of other set.

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Keywords

• Approximation space
• T-rough set
• T-rough fuzzy set
• Fuzzy subgroups
• Fuzzy ideals
• set-valued homomorphism.

MSC

•  20N25
•  20E07

References

• [1] M. Banerjee, S. K. Pal , Roughness of a fuzzy set , Inform. Sci., 93 (1996), 235-246.
  • View Article
  • Google Scholar


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


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


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


• [5] B. Davvaz, A short note on algebraic T-rough sets , Information Sciences , Vol.17 (2008), 3247-3252.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [6] B. Davvaz, Roughness in rings, Inform. Sci. , 164 (2004), 147-163.
  • View Article
  • MathSciNet
  • Google Scholar


• [7] D. Dubois, H. Prade , Rough fuzzy sets and fuzzy rough sets, Int. J. General Syst., 17 (2-3) (1990), 191-209.
  • View Article
  • Google Scholar


• [8] D. Dubois, H. Prade , Two fold fuzzy sets and rough sets-some issues in knowledge representation, Fuzzy Sets Syst. 23, 3-18. (1987)
  • View Article
  • Google Scholar


• [9] E. Ranjbar-Yanehsari, M. Asghari-Larimi , union and intersection fuzzy subhypergroups, JMCS, 5(2) (2012), 82-90.
  • Google Scholar


• [10] E. Hendukolaie, On fuzzy homomorphism between hypernear-rings, JMCS, 2(4) (2011), 702-716.
  • Google Scholar


• [11] E. Hendukolaie , M. Aliakbarnia Omran, Y. Nasabi , On fuzzy isomorphism theorems of \(\Gamma\)- hypernear-rings, JMCS, 7 (2013), 80-88.
  • Google Scholar


• [12] S. B. Hosseini, N. Jafarzadeh, A. Gholami, T-rough Ideal and T-rough Fuzzy Ideal in a Semigrou , Advanced Materials Research, 433-440 (2012), 4915-4919.
  • View Article
  • Google Scholar


• [13] S. B. Hosseini, N. Jafarzadeh, A. Gholami, Some Results on T-rough (prime, primary) Ideal and T-rough Fuzzy (prime, primary) Ideal on Commutative Rings , Int.J.Contemp. Math Scince, 7 (2012), 337-350.
  • Google Scholar


• [14] T. Iwinski, Algebraic approach to rough sets, Bull. PolishAcad. Sci. Math., 35 (1987), 673-683.
  • MathSciNet
  • Google Scholar


• [15] O. Kazanci , B. Davvaz, On the structure of rough prime (primary) ideals and rough fuzzy prime (primary) ideals in commutative rings, Information Sciences, 178 (2008), 1343-1354.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [16] N. Kuroki , Rough ideals in semigroups, Inform. Sci. , 100 (1997), 139-163.
  • View Article
  • Google Scholar


• [17] W. J. Liu , Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets Syst. , 8 (1982), 133–139.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [18] J. N. Mordeson, M. S. Malik , Fuzzy Commutative Algebra , World Publishing, Singapore (1998)
  • Google Scholar


• [19] A. Nakamura, Fuzzy rough sets , Note on Multiple-valued Logic in Japan, 9 (8) (1988), 1-8.
  • View Article
  • Google Scholar


• [20] S. Nanda, Fuzzy rough sets, Fuzzy Sets and Systems, 45 (1992), 157-160.
  • View Article
  • Google Scholar


• [21] Z. Pawlak, Rough sets, Int. J. Inform. Comput. Sci. , 11 (1982), 341-356.
  • View Article
  • Google Scholar


• [22] Z. Pawlak, Rough sets- Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishing, Dordrecht (1991)
  • Google Scholar


• [23] Z. Pawlak, Rough sets power set hierarchy, ICS PAS Rep., 470 (1982),
  • Google Scholar


• [24] Z. Pawlak, Rough sets algebraic and topological approach, ICS PAS Rep., 482 (1982),


• [25] Z. Pawlak, Rough sets and fuzzy sets , Fuzzy Sets and Systems, 17 (1985), 99-102.
  • View Article
  • Google Scholar


• [26] Z. Pawlak, Some remarks on rough sets, Bull. Pol. Acad.Tech. 33, (1985)
  • MathSciNet


• [27] Z. Pawlak, A. Skowron , Rough sets and Boolean reasoning, Information Sciences, 177 (2007), 41-73.
  • View Article
  • MathSciNet
  • Google Scholar


• [28] Z. Pawlak, A. Skowron , Rough sets: some extensions, Information Science, 177 (2007), 28-40.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [29] A. Rosenfeild, Fuzzy Groups, Journal of Mathematical Analysis and Application , 35 (1971), 512-517.
  • Google Scholar


• [30] Q. M. Xiao, Z. L. Zhang, Rough prime ideals and rough fuzzy prime ideals in semigroups, Information Sciences, 176 (2006), 725-733.
  • View Article
  • Google Scholar


• [31] S. Yamak, O. Kazanci, B. Davvaz, Generalized lower and upper approximations in a ring , Information Sciences , 180 (2010), 1759-1768.
  • View Article
  • MathSciNet
  • Google Scholar


• [32] L. A. Zadeh, Fuzzy sets, Inform. Control , 8 (1965), 338-353.
  • Google Scholar