Soft set theory, proposed by Molodtsov, has been regarded as a generic mathematical tool for dealing with uncertainties. However, classical soft sets are not appropriate to deal with incomplete and inconsistent information. In this paper, we introduce the concept of paraconsistent soft sets combining paraconsistent logic and soft sets. The complement, “And”, restricted intersection, relaxed intersection, restricted cross and relaxed cross operations are defined on paraconsistent soft sets. In order to deal with incomplete and inconsistent information in decision making simultaneously, we also define paraconsistent soft decision system, choice value, decision value, the selected set and the eliminated set, and bring up the decision algorithm. Finally, an investment decision problem with incomplete and inconsistent information is analyzed by paraconsistent soft sets. The result shows that paraconsistent soft sets with more adequate parameterization can solve decision making problems with incomplete and inconsistent information more effectively than classical soft sets.
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