Ideal Theory of BCK/BCI-algebras Based on Double-framed Soft Sets

The notion of a (closed) double-framed soft ideal (briefly, a (closed ) DFS-ideal) in BCK/BCI-algebras is introduced, and related properties are investigated. Several examples are provided. T he relation between a DFS-algebra and a DFS-ideal is considered, and characterizations of a (closed) DFS-ideal are established. A new DFS-ideal from old one is constructed, and we show that the int-uni DFS-set of two DFS-ideals is a DFS-ideal. Conditions for a DFS-ideal to be closed are discussed.

[1]  Young Bae Jun,et al.  Applications of soft sets in ideal theory of BCK/BCI-algebras , 2008, Inf. Sci..

[2]  Bekir Tanay,et al.  Computers and Mathematics with Applications , 2022 .

[3]  A. Iorgulescu,et al.  Algebras of Logic as BCK Algebras , 2008 .

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

[5]  Young Bae Jun,et al.  Soft ordered semigroups , 2010, Math. Log. Q..

[6]  Jianming Zhan,et al.  Soft p-ideals of soft BCI-algebras , 2009, Comput. Math. Appl..

[7]  Bobby Schmidt,et al.  Fuzzy math , 2001 .

[8]  Jianming Zhan,et al.  Soft R0-Algebras Based on Fuzzy Sets , 2010, J. Multiple Valued Log. Soft Comput..

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

[10]  Young Bae Jun,et al.  Double-Framed Soft Sets with Applications in BCK/BCI-Algebras , 2012, J. Appl. Math..

[11]  Wieslaw A. Dudek,et al.  Soft MTL-algebras based on fuzzy sets , 2010 .

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

[13]  Feng Feng,et al.  Soft rough sets applied to multicriteria group decision making , 2011 .

[14]  Young Bae Jun,et al.  Pseudo d-algebras , 2009, Inf. Sci..

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

[16]  Young Bae Jun,et al.  Soft BCK/BCI-algebras , 2008, Comput. Math. Appl..

[17]  Aslihan Sezgin Sezer,et al.  Soft substructures of rings, fields and modules , 2011, Comput. Math. Appl..

[18]  Y. Jun,et al.  SOFT WS-ALGEBRAS , 2008 .

[19]  IorgulescuAfrodita.  On BCK algebras , 2008, SOCO 2008.

[20]  Naim Ca ˘ Filiz.  FP-soft set theory and its applications , 2011 .

[21]  Young Bae Jun,et al.  Soft set theory applied to ideals in d-algebras , 2009, Comput. Math. Appl..