Generalized roughness in (∈,∈∨q)-fuzzy ideals of hemirings

Authors

  • Muhammad Rameez Riphah International University Islamabad
  • Muhammad Irfan Ali Islamabad Model College for Girls F-6/2, Islamabad.
  • Asad Ejaz Riphah International University Islamabad

Keywords:

Fuzzy sets, Rough sets, Semirings, Ideals, fuzzy ideals.

Abstract

Generalized roughness for fuzzy ideals in hemirings is studied. Approximations for fuzzy prime ideals are discussed. It is shown that generalized lower approximation as well as generalized upper approximation of (∈ , ∈∨q)-fuzzy prime (semiprime) ideals of hemirings are (∈ , ∈∨q) fuzzy prime (semiprime) ideals.

Author Biographies

Muhammad Rameez, Riphah International University Islamabad

Department of Mathematics and Student

Muhammad Irfan Ali, Islamabad Model College for Girls F-6/2, Islamabad.

Department of Mathematics and Associate Professor

Asad Ejaz, Riphah International University Islamabad

Department of Mathematics and student

References

J. Ahsan, K. Saifullah, M.F. Khan,(1993). Fuzzy semirings, Fuzzy Sets and Systems, 60, 309--320.

S.K. Bhakat and P. Das,(1992). On the definition of a fuzzy subgroup, Fuzzy Sets and Systems, 51, 235-241.

R. Biswas and S. Nanda,(1994). Rough groups and Rough subgroups, Bull. Polish Acad. of Sciences Vol. 42 No. 3.1.

B. Davvaz (2008). A short note on algebraic T-rough sets. Inf Sci 178, 3247-3252.

B. Davvaz and M. Mahdavipour, (2006). Roughness in modules, Information Sciences, 176, 3658-3674.

Dubois and Prade, (1990). Rough fuzzy sets and fuzzy rough sets.International Journal of General Systems,17, 191--208.

W.A. Dudek, M. Shabir, M.I. Ali, (2009). (α,β)-fuzzy ideals of hemirings, Comput. Math. Appl. 58, 310--321.

M.I. Ali, M. Shabir, S. Tanveer, (2012). Roughness in hemirings, Neural Comput & Appl. 21, (Suppl 1):S171--S180.

J.S. Golan, The Theory of Semirings with applications in Mathematics and Theoretical Computer Science, Pitman Monographs and Surveys in Pure and App. Maths., no. 54 (Longman, New York, 1992).

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

S.B. Hosseini, N, Jafarzadeh,(2012). 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, Vol.7, 337-350.

T.B. Iwinski, (1987). Algebraic Approach to Rough Sets, Bull. Polish Acad.,Vol. 35, No 9-10.

K. Iizuka, (1959). On jacobson radical of hemirings, Tohoku Math. J. 11 (2), 409-421.

Y.B. Jun, (2003). Roughness of ideals in BCK-algebra, Scientiae Math. Japonica, 57(1), 165-169.

O. Kazanci, B. Davvaz, (2008). On the structure of rough prime (primary) ideals and rough fuzzy prime (primary) ideals in commutative rings, Information Sciences, 178, 1343-1354.

C.B. Kim, M. Park, (1996). k-fuzzy ideals in semirings, Fuzzy Sets Systems 81, 281--286.

N. Kuroki,(1997). Rough ideals in Semigroups, Information Sciences, 100 139-163.

N. Kuroki and P.P. Wang,(1996). The lower and upper approximations in a fuzzy group, Information Sciences, 90, 203-220.

K. Iizuka (1959), On jacobson radical of hemirings.Tohoku Math J 11(2):409--421.

P.P. Ming and L.Y. Ming, (1980). Fuzzy topology I: Neighbourhood structure of a fuzzy point and Moore-Smith convergence, J. Math.Anal. Appl. 76, 571-599.

Z. Pawlak (1982). Rough Sets. Int J Compsci 11:341-356.

Z. Pawlak, Rough Sets theoretical aspects of reasoning about data, Kluwer Academic Publisher, 1991.

S. Yamak, O. Kazanci,B. Davaz, (2010). Generalized lower and upper approximations in a ring, Information Sciences, 180, 1759-1768.

L.A. Zadeh,(1965). Fuzzy Sets, Inf. Control 8 339-353.

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Published

21-07-2017