Subalgebras of BCK/BCI-Algebras Based on Cubic Soft Sets

Operations of cubic soft sets including “AND” operation and “OR” operation based on P-orders and R-orders are introduced and some related properties are investigated. An example is presented to show that the R-union of two internal cubic soft sets might not be internal. A sufficient condition is provided, which ensure that the R-union of two internal cubic soft sets is also internal. Moreover, some properties of cubic soft subalgebras of BCK/BCI-algebras based on a given parameter are discussed.

[1]  Young Bae Jun,et al.  Fuzzy soft set theory applied to BCK/BCI-algebras , 2010, Comput. Math. Appl..

[2]  Yan Zou,et al.  Data analysis approaches of soft sets under incomplete information , 2008, Knowl. Based Syst..

[3]  Feng Feng,et al.  Soft subsets and soft product operations , 2013, Inf. Sci..

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

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

[6]  Muhammad Irfan Ali,et al.  A note on soft sets, rough soft sets and fuzzy soft sets , 2011, Appl. Soft Comput..

[7]  Naim Çagman,et al.  Soft set theory and uni-int decision making , 2010, Eur. J. Oper. Res..

[8]  Chyi Hwang,et al.  An FFT-based algorithm for 2D power series expansions , 1999 .

[9]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[10]  Xia Zhang,et al.  The bijective soft set with its operations , 2010, Comput. Math. Appl..

[11]  Feng Feng,et al.  Generalized uni-int decision making schemes based on choice value soft sets , 2012, Eur. J. Oper. Res..

[12]  K. V. Babitha,et al.  Soft set relations and functions , 2010, Comput. Math. Appl..

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

[14]  M. Gorzałczany A method for inference in approximate reasoning based on interval-valued fuzzy sets , 1987 .

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

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

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

[18]  Abdullah M. Al-roqi,et al.  Cubic soft sets with applications in BCK/BCI-algebras , 2014 .

[19]  Muhammad Akram,et al.  Applications of Soft Sets in K-Algebras , 2013, Adv. Fuzzy Syst..

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

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

[22]  Andrzej Skowron,et al.  Rudiments of rough sets , 2007, Inf. Sci..

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

[24]  Feng Feng,et al.  Soft intersection Lie algebras , 2013 .

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

[26]  Young Bae Jun,et al.  Cubic structures applied to ideals of BCI-algebras , 2011, Comput. Math. Appl..