Fuzzy Gamma-hypernear-rings

The concept of @C-hypernear-rings, which is a generalization of @C-near-rings and hypernear-rings, is introduced. Some related properties of @C-hypernear-rings are described. In particular, three Isomorphism Theorems of @C-hypernear-rings are established. By using this new idea, we consider the fuzzy hyperideals of @C-hypernear-rings. Finally, the fundamental relations between @C-hypernear-rings and @C-near-rings are discussed.

[1]  Günter Pilz,et al.  Near-rings : the theory and its applications , 1983 .

[2]  Bijan Davvaz,et al.  (∈, ∈ ∨ q)-fuzzy subnear-rings and ideals , 2006, Soft Comput..

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

[4]  T. K. Dutta,et al.  On fuzzy congruence of a near-ring module , 2000, Fuzzy Sets Syst..

[5]  Bijan Davvaz,et al.  Generalized fuzzy hyperideals of hypernear-rings and many valued implications , 2006, J. Intell. Fuzzy Syst..

[6]  Young Bae Jun,et al.  Normal fuzzy R-subgroups in near-rings , 2001, Fuzzy Sets Syst..

[7]  Jianming Zhan,et al.  On properties of fuzzy hyperideals in hypernear-rings with t-Norms , 2006 .

[8]  Fabrizio Durante,et al.  Copula Theory and Its Applications , 2010 .

[9]  Salah Abou-Zaid On fuzzy subnear-rings and ideals , 1991 .

[10]  B. Davvaz,et al.  ON HYPER R-SUBGROUPS OF HYPERNEAR-RINGS , 2008 .

[11]  Hee Sik Kim,et al.  On fuzzy ideals of near-rings , 1996 .

[12]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[13]  B. Davaz FUZZY IDEALS OF NEAR-RINGS WITH INTERVAL VALUED MEMBERSHIP FUNCTIONS , 2001 .

[14]  Jianming Zhan,et al.  Generalized fuzzy Hv-submodules endowed with interval valued membership functions , 2008, Inf. Sci..

[15]  Malaysian Mathematical,et al.  Structures of Fuzzy Ideals of -Ring , 2005 .

[16]  Bijan Davvaz,et al.  T-FUZZY SUBHYPERNEAR-RINGS OF HYPERNEAR-RINGS , 2005 .

[17]  Jianming Zhan,et al.  A new view of fuzzy hypernear-rings , 2008, Inf. Sci..

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

[19]  Violeta Leoreanu Fotea,et al.  Isomorphisms of hypergroups and of n-hypergroups with applications , 2009, Soft Comput..