ON GENERALIZED ROUGH ( m , n )-BI-Γ-HYPERIDEALS IN Γ-SEMIHYPERGROUPS

Recently, in [12], Yaqoob et al. introduced the notion of (m,n)-bi-Γhyperideals and applied the concept of rough set theory to (m,n)-bi-Γ-hyperideals, which is a generalization of (m,n)-bi-Γ-hyperideals of Γ-semihypergroups. In this paper, applying the rough set theory based on an arbitrary binary relation (not an equivalent relation) we extend and generalize these notions, introducing the notion of generalized rough (m, 0)-Γ-hyperideals (generalized rough (0, n)-Γ-hyperideals), generalized rough (m,n)-quasi and bi-Γ-hyperideals and generalized rough m-left Γ-hyperideals) and establish some of their basic properties in Γ-semihypergroups.

[1]  Christina Gloeckner,et al.  Applications Of Hyperstructure Theory , 2016 .

[2]  L. Polkowski.  Rough Sets: Mathematical Foundations , 2013 .

[3]  B. Davvaz,et al.  Semihypergroups and Regular Relations , 2013 .

[4]  N. Yaqoob,et al.  ON ROUGH ( m , n ) BI-Γ-HYPERIDEALS IN Γ-SEMIHYPERGROUPS , 2013 .

[5]  B. Davvaz,et al.  Study on the Structure of Γ-Semihypergroups , 2012 .

[6]  Bijan Davvaz,et al.  On Quasi-Hyperideals in Semihypergroups , 2011 .

[7]  Aslam.  Roughness in Left Almost Semigroups , 2011 .

[8]  Muhammad Shabir,et al.  On rough ( m , n )-bi-ideals and generalized rough ( m , n )-bi-ideals in semigroups , 2011 .

[9]  Bijan Davvaz,et al.  On -hyperideals in -semihypergroups , 2010 .

[10]  Paul P. Wang,et al.  Comment on “The lower and upper approximations in a fuzzy group” , 1996, 2009 International Conference on Machine Learning and Cybernetics.

[11]  Yong Chan Kim,et al.  Generalized Rough Sets and Relations , 2009 .

[12]  Violeta Leoreanu Fotea,et al.  The lower and upper approximations in a hypergroup , 2008, Inf. Sci..

[13]  Bijan Davvaz,et al.  Rough approximations in a general approximation space and their fundamental properties , 2008, Int. J. Gen. Syst..

[14]  Bijan Davvaz,et al.  The lower and upper approximations in a quotient hypermodule with respect to fuzzy sets , 2008, Inf. Sci..

[15]  Bijan Davvaz,et al.  On the structure of rough prime (primary) ideals and rough fuzzy prime (primary) ideals in commutative rings , 2008, Inf. Sci..

[16]  Bijan Davvaz,et al.  Approximations in n-ary algebraic systems , 2008, Soft Comput..

[17]  Bijan Davvaz,et al.  Roughness in modules , 2006, Inf. Sci..

[18]  Bijan Davvaz,et al.  Rough subpolygroups in a factor polygroup , 2006, J. Intell. Fuzzy Syst..

[19]  Bijan Davvaz,et al.  A New view of the approximations in Hv-groups , 2006, Soft Comput..

[20]  Michiro Kondo,et al.  On the structure of generalized rough sets , 2006, Inf. Sci..

[21]  Qi-Mei Xiao,et al.  Rough prime ideals and rough fuzzy prime ideals in semigroups , 2006, Inf. Sci..

[22]  Bijan Davvaz,et al.  Roughness in rings , 2004, Inf. Sci..

[23]  Gianpiero Cattaneo,et al.  Algebraic Structures for Rough Sets , 2004, Trans. Rough Sets.

[24]  Y B Jun,et al.  ROUGHNESS OF GAMMASUBSEMI GROUPS/IDEALS IN GAMMA-SEMIGROUPS , 2003 .

[25]  J. Bae.  ROUGHNESS OF IDEALS IN BCK-ALGEBRAS , 2003 .

[26]  Piergiulio Corsini,et al.  Fuzzy sets and join spaces associated with rough sets , 2002 .

[27]  B. Davvaz.  APPROXIMATIONS IN Hv-MODULES , 2002 .

[28]  Yiyu Yao,et al.  Information granulation and rough set approximation , 2001, Int. J. Intell. Syst..

[29]  Yiyu Yao,et al.  Constructive and Algebraic Methods of the Theory of Rough Sets , 1998, Inf. Sci..

[30]  Yiyu Yao,et al.  On Generalizing Pawlak Approximation Operators , 1998, Rough Sets and Current Trends in Computing.

[31]  Y. Yao,et al.  Generalized Rough Set Models , 1998 .

[32]  Nobuaki Kuroki,et al.  Rough Ideals in Semigroups , 1997, Inf. Sci..

[33]  Janusz Zalewski,et al.  Rough sets: Theoretical aspects of reasoning about data , 1996 .

[34]  Yiyu Yao,et al.  Generalization of Rough Sets using Modal Logics , 1996, Intell. Autom. Soft Comput..

[35]  T. Iwiński.  Algebraic approach to rough sets , 1987 .

[36]  F. Marty.  Sur une generalization de la notion de groupe , 1934 .