Topological Structures of Lower and Upper Rough Subsets in a Hyperring

In this paper, we study the connection between topological spaces, hyperrings (semi-hypergroups), and rough sets. We concentrate here on the topological parts of the lower and upper approximations of hyperideals in hyperrings and semi-hypergroups. We provide the conditions for the boundary of hyp-ideals of a hyp-ring to become the hyp-ideals of hyp-ring.

[1]  S. Yamak,et al.  A note on the lattice of fuzzy hyperideals of a hyperring , 2017 .

[2]  Jianming Zhan,et al.  On Rough Hyperideals in Hyperlattices , 2013, J. Appl. Math..

[3]  N. Yaqoob,et al.  Rough Hyperfilters in Po-LA-Semihypergroups , 2019 .

[4]  K. Hila,et al.  On Hyperideals in Left Almost Semihypergroups , 2011 .

[5]  M. Shabir,et al.  Roughness in ordered Semigroups , 2013 .

[6]  Bijan Davvaz,et al.  Fuzzy hyperrings , 2009, Fuzzy Sets Syst..

[7]  R. Ameri,et al.  Approximations in (bi-)hyperideals of Semihypergroups , 2013 .

[8]  A. Ghareeb.  Degree of F-irresolute function in (L, M)-fuzzy topological spaces , 2019 .

[9]  Bijan Davvaz,et al.  Pawlak's approximations in Gamma-semihypergroups , 2010, Comput. Math. Appl..

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

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

[12]  B. Davvaz,et al.  Γ-semihyperrings: Approximations and rough ideals , 2011 .

[13]  S. Ahn,et al.  ROUGH SET THEORY APPLIED TO FUZZY FILTERS IN BE-ALGEBRAS , 2016 .

[14]  Xiongwei Zhang,et al.  Measurement of Countable Compactness and Lindelöf Property in RL -Fuzzy Topological Spaces , 2021, Complex..

[15]  Wen-Ran Zhang,et al.  Bipolar Fuzzy Sets , 1997 .

[16]  D. Molodtsov.  Soft set theory—First results , 1999 .

[17]  Muhammad Shabir,et al.  Roughness in quantale modules , 2018, J. Intell. Fuzzy Syst..

[18]  N. Yaqoob,et al.  On Intra-Regular Left Almost Semihypergroups with Pure Left Identity , 2012, 1211.5588.

[19]  Zdzis?aw Pawlak,et al.  Rough sets , 2005, International Journal of Computer & Information Sciences.

[20]  Yanfeng Luo,et al.  Hyperfilters and fuzzy hyperfilters of ordered semihypergroups , 2015, J. Intell. Fuzzy Syst..

[21]  Tahir Mahmood,et al.  A study of generalized roughness in -fuzzy filters of ordered semigroups , 2018 .

[22]  Muhammad Shabir,et al.  Generalized Rough Fuzzy Ideals in Quantales , 2018 .

[23]  Florentin Smarandache,et al.  Neutrosophic set - a generalization of the intuitionistic fuzzy set , 2004, 2006 IEEE International Conference on Granular Computing.

[24]  Bijan Davvaz,et al.  Fuzzy Krasner (m, n)-hyperrings , 2010, Comput. Math. Appl..

[25]  R. Ameri,et al.  Fuzzy Hyperideals of Fuzzy Hyperrings , 2012 .

[26]  Redundancy of multiset topological spaces , 2016, 1606.01150.

[27]  P. Corsini,et al.  Applications of Hyperstructure Theory , 2010 .

[28]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[29]  N. Yaqoob,et al.  Partially ordered left almost semihypergroups , 2015 .