On Some New Operations in Probabilistic Soft Set Theory

In this paper, we study the theory of probabilistic soft sets introduced by Zhu and Wen \cite{ZhuWen}. We define equality of two probabilistic soft sets, subset, complement of a probabilistic soft set, impossible probabilistic soft set, certain probabilistic soft set with examples.We also introduce the operations of union, intersection, difference and symmetric difference. We prove that certain De Morgan's laws hold in probabilistic soft set theory with respect to these new definitions.

[1]  Naim Çag ˘ man,et al.  Soft set theory and uni-int decision making , 2010 .

[2]  Aslihan Sezgin Sezer,et al.  On operations of soft sets , 2011, Comput. Math. Appl..

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

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

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

[6]  Qiaoyan Wen,et al.  Probabilistic Soft Sets , 2010, 2010 IEEE International Conference on Granular Computing.

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