Ideal Theory in Semigroups Based on Intersectional Soft Sets

The notions of int-soft semigroups and int-soft left (resp., right) ideals are introduced, and several properties are investigated. Using these notions and the notion of inclusive set, characterizations of subsemigroups and left (resp., right) ideals are considered. Using the notion of int-soft products, characterizations of int-soft semigroups and int-soft left (resp., right) ideals are discussed. We prove that the soft intersection of int-soft left (resp., right) ideals (resp., int-soft semigroups) is also int-soft left (resp., right) ideals (resp., int-soft semigroups). The concept of int-soft quasi-ideals is also introduced, and characterization of a regular semigroup is discussed.

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

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

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

[4]  M. Shabir,et al.  Soft relations applied to semigroups , 2013 .

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

[6]  Jianming Zhan,et al.  Applications of soft union sets to hemirings via SU-h-ideals , 2014, J. Intell. Fuzzy Syst..

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

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

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

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

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

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

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

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

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

[16]  Y. Jun,et al.  Intersectional soft BCK/BCI-ideals , 2012 .

[17]  Feng Feng,et al.  Application of level soft sets in decision making based on interval-valued fuzzy soft sets , 2010, Comput. Math. Appl..

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

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

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

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

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

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

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

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

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

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

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