Rough set approach to non-cooperative continuous differential games

In this article, we analyze the non-cooperative continuous differential games under rough interval environment. The combination of rough set and continuous differential games expresses a new class defined as rough non-cooperative continuous differential games. We develop an effective and simple technique for solving the problem under study; in this methodology, the rough non-cooperative continuous differential games are transformed into two problems with interval environment corresponding to the upper and lower approximation of rough intervals. Furthermore, four crisp problems of non-cooperative continuous differential games are derived as follows: upper lower problem (ULP), lower lower problem (LLP), lower upper problem (LUP) and upper upper problem (UUP). Moreover, the trust measure and the expected value operator of rough interval are used to find the α-trust equilibrium strategies and the expected equilibrium strategies. Sufficient and necessary conditions for equilibrium strategies of rough non-cooperative continuous differential games are also derived. Finally, applicability and validity of the models and technique proposed in this article are illustrated with a practical example.