Lattice Structures of Fuzzy Soft Sets

In this paper, we study the algebraic structures of fuzzy soft sets. Some operations on fuzzy soft sets are introduced and several related properties are investigated. Furthermore, two lattice structures of fuzzy soft sets are established. It is proved that certain De Morgan's laws hold in fuzzy soft set theory.

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

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

[3]  Tsau Young Lin,et al.  Combination of interval-valued fuzzy set and soft set , 2009, Comput. Math. Appl..

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

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

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

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

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

[9]  Pabitra Kumar Maji,et al.  FUZZY SOFT SETS , 2001 .

[10]  Zhi Xiao,et al.  A combined forecasting approach based on fuzzy soft sets , 2009 .

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

[12]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..