Measurable Soft Sets

The soft set is a mapping from a parameter to the crisp subset of universe. Molodtsov introduced the concept of soft sets as a generalized tool for modeling complex systems involving uncertain or not clearly defined objects. In this paper the concept of measurable soft sets are introduced and their properties are discussed. The open problem of this paper is to develop measurable functions and lebesgue integral in soft set theory context.

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

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

[3]  Yan Zou,et al.  Exclusive disjunctive soft sets , 2010, Comput. Math. Appl..

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

[5]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

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

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

[8]  Steven Li,et al.  The normal parameter reduction of soft sets and its algorithm , 2008, Comput. Math. Appl..

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

[10]  Keyun Qin,et al.  On soft equality , 2010, J. Comput. Appl. Math..

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

[12]  W.-L. Gau,et al.  Vague sets , 1993, IEEE Trans. Syst. Man Cybern..

[13]  K. Atanassov Operators over interval valued intuitionistic fuzzy sets , 1994 .

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

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

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

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

[18]  Muhammad Shabir,et al.  On soft topological spaces , 2011, Comput. Math. Appl..

[19]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .