Another approach to rough soft hemirings and corresponding decision making

Combining rough sets and soft sets, a kind of novel rough soft hemirings with respect to a strong h-ideal of hemirings in Pawlak approximation spaces is introduced. The relationships between lower and upper rough soft hemirings are studied. In particular, lower and upper rough soft strong h-ideals with respect to strong h-ideals are investigated, respectively. Some good examples are given. Finally, we put forward two new kinds of decision-making methods in rough soft sets, and some related algebraic and applied examples are also given.

[1]  Jianming Zhan,et al.  The characterizations of hemirings in terms of fuzzy soft h-ideals , 2011, Neural Computing and Applications.

[2]  Lei Zhang,et al.  Boundary integral equation methods for the scattering problem by an unbounded sound soft rough surface with tapered wave incidence , 2015, J. Comput. Appl. Math..

[3]  Jianhua Dai,et al.  On the union and intersection operations of rough sets based on various approximation spaces , 2015, Inf. Sci..

[4]  Naim Çagman,et al.  Soft sets and soft groups , 2007, Inf. Sci..

[5]  William Zhu,et al.  The algebraic structures of generalized rough set theory , 2008, Inf. Sci..

[6]  Kenzo Iizuka,et al.  On the Jacobson radical of a semiring , 1959 .

[7]  Jianming Zhan,et al.  A new rough set theory: rough soft hemirings , 2015, J. Intell. Fuzzy Syst..

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

[9]  Wieslaw A. Dudek,et al.  (alpha, Beta)-fuzzy Ideals of Hemirings , 2009, Comput. Math. Appl..

[10]  Young Bae Jun,et al.  *-μ-semirings and *-λ-semirings , 2005, Theor. Comput. Sci..

[11]  Young Bae Jun,et al.  Soft semirings , 2008, Comput. Math. Appl..

[12]  Yiyu Yao,et al.  Covering based rough set approximations , 2012, Inf. Sci..

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

[14]  Jianming Zhan,et al.  Fuzzy parameterized fuzzy soft h-ideals of hemirings , 2014, Journal of Intelligent & Fuzzy Systems.

[15]  Zhoujun Li,et al.  A novel variable precision (θ, σ)-fuzzy rough set model based on fuzzy granules , 2014, Fuzzy Sets Syst..

[16]  A. R. Roy,et al.  A fuzzy soft set theoretic approach to decision making problems , 2007 .

[17]  Bijan Davvaz,et al.  (alpha, Beta)-intuitionistic Fuzzy Ideals of Hemirings , 2011, Comput. Math. Appl..

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

[19]  William Zhu,et al.  Rough matroids based on relations , 2013, Inf. Sci..

[20]  Degang Chen,et al.  Rough approximation of a fuzzy concept on a hybrid attribute information system and its uncertainty measure , 2014, Inf. Sci..

[21]  Lihua Dong Fuzzy k-ideals in Semirings Redefined , 2002 .

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

[23]  Muhammad Irfan Ali,et al.  Roughness in hemirings , 2011, Neural Computing and Applications.

[24]  Zhiming Zhang,et al.  A rough set approach to intuitionistic fuzzy soft set based decision making , 2012 .

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

[26]  William Zhu,et al.  Relationship among basic concepts in covering-based rough sets , 2009, Inf. Sci..

[27]  Eric C. C. Tsang,et al.  The parameterization reduction of soft sets and its applications , 2005 .

[28]  Xiaoyan Liu,et al.  On some new operations in soft set theory , 2009, Comput. Math. Appl..

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

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

[31]  Yiyu Yao,et al.  Three-way decisions with probabilistic rough sets , 2010, Inf. Sci..

[32]  Jianhua Dai,et al.  Rough 3-valued algebras , 2008, Inf. Sci..

[33]  Shamik Ghosh,et al.  Matices over Semirings , 1996, Inf. Sci..

[34]  Dan Meng,et al.  Soft rough fuzzy sets and soft fuzzy rough sets , 2011, Comput. Math. Appl..

[35]  Yiyu Yao,et al.  Quantitative rough sets based on subsethood measures , 2014, Inf. Sci..

[36]  Young Bae Jun,et al.  On fuzzy h-ideals in hemirings , 2004, Inf. Sci..

[37]  Young Bae Jun,et al.  An adjustable approach to fuzzy soft set based decision making , 2010, J. Comput. Appl. Math..

[38]  Chang Bum Kim,et al.  k-Fuzzy ideals in semirings , 1996, Fuzzy Sets Syst..

[39]  Young Bae Jun,et al.  Soft sets and soft rough sets , 2011, Inf. Sci..

[40]  A. R. Roy,et al.  An application of soft sets in a decision making problem , 2002 .

[41]  Jianming Zhan,et al.  Fuzzy h-ideals in h-hemiregular and h-semisimple $$\Upgamma$$-hemirings , 2010, Neural Computing and Applications.

[42]  Bijan Davvaz,et al.  Soft sets combined with fuzzy sets and rough sets: a tentative approach , 2010, Soft Comput..

[43]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

[44]  Qingguo Li,et al.  Rough sets induced by ideals in lattices , 2014, Inf. Sci..

[45]  Bijan Davvaz,et al.  Generalized lower and upper approximations in a ring , 2010, Inf. Sci..

[46]  A. R. Roy,et al.  Soft set theory , 2003 .