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.

Paraconsistent soft sets can address issues involving incomplete and inconsistent information simultaneously. In this paper, paraconsistent soft sets are furtherly extended to dynamic paraconsistent soft sets by introducing time factors. We define some basic operations, such as dynamic paraconsistent soft subsets, complement, "AND", restricted intersection, relaxed intersection, restricted cross and relaxed cross. Subsequently, we also propose the definitions of dynamic paraconsistent soft decision system, compound time choice value, compound time decision value, compound time weighting vector and final decision value. Additionally, we construct a decision making algorithm for dynamic paraconsistent soft sets, which can address issues involving both dynamic incomplete and inconsistent information. Furthermore, we apply the proposed algorithm to a practical loan problem for small and micro enterprises. Finally, we perform a sensitivity analysis and a comparative analysis to prove the effectiveness and feasibility of the proposed algorithm.