A trust-region based an active-set interior-point algorithm for fuzzy continuous Static Games

In this paper, a novel treatment for fuzzy continuous static games (FCSGs) is introduced. This treatment is based on the fact that, as well as having a fuzzy number, the fuzziness is applied to the control vectors to deal with high vagueness and imprecision in a continuous static game. The concept of the $\alpha$-level set used for converting the FCSGs to a deterministic problem $\alpha$-FCSGs. An active-set strategy is used with Newton's interior point method and a trust-region strategy to insure global convergence for deterministic $\alpha$-FCSGs problems from any starting point. A reduced Hessian technique is used to overcome the difficulty of having an infeasible trust-region subproblem. The active-set interior-point trust-region algorithm has new features; it is easy to implement and has rapid convergence. Preliminary numerical results are reported.