Generalization of soft set theory: From crisp to fuzzy case

The traditional soft set is a mapping from parameter to the crisp subset of universe. However, the situation may be more complex in real world because the fuzzy characters of parameters. In this paper, the traditional soft set theory is expanded to be a fuzzy one, the fuzzy membership is used to describe parameter-approximate elements of fuzzy soft set. Furthermore, basic fuzzy logic operators are used to define generalized operators on fuzzy soft set and then the DeMorgan's laws are proved. Finally, the parametrization reduction of fuzzy soft set is defined, a decision-making problem is analyzed to indicate the validity of the fuzzy soft set.