Probabilistic soft sets and dual probabilistic soft sets in decision-making

Since its introduction by Molodstov (Computers & Mathematics with Applications 37(4):19-31 1999), soft set theory has been widely applied in various fields of study. Soft set theory has also been combined with other theories like fuzzy sets theory, rough sets theory, and probability theory. The combination of soft sets and probability theory generates probabilistic soft set theory. However, decision-making based on the probabilistic soft set theory has not been discussed in the literature. In this paper, we propose new algorithms for decision-making based on the probabilistic soft set theory. An example to show the application of these algorithms is given, and its possible extensions and reinterpretations are discussed. Inspired by realistic situations, the notion of dual probabilistic soft sets is proposed, and also, its application in decision-making is investigated.