In order to further improve the cooperative performance of evolutionary populations to solve out the optimal solution for attribute reduction in rough set theory

a novel attribute equilibrium reduction algorithm(named AERQG)with quantum game based on mixed co-evolutionary populations' collaboration is proposed.In this algorithm

the collaboration model of co-evolutionary populations based on the self-adaptive multilevel evolutionary tree is constructed.The mixed co-evolutionary mechanism

which is both competitive co-evolution for evolutionary individuals in populations and cooperative co-evolution for representative elitists between populations

is adopted to carry out the populations' co-evolution.This mechanism can better obtain the balance of attribute co-evolutionary reduction between exploitation in breadth and exploration in depth.Moreover

the compensation mechanism of trust margin is introduced into the quantum game model for multi-populations elites.The population elite can be sure to find out the respective optimal subset of attribute reduction by using the quantum game strategy

and thus the global optimal collaboration set of attribute reduction under the Nash equilibrium is achieved steadily.Experimental results demonstrate the proposed algorithm has achieved better high-performance on efficiency and accuracy than traditional algorithms.Further

the efficient reduction and segmentation for brain magnetic resonance imaging(MRI)in the incomplete electronic medical record system verifies its stronger practicality and robustness.