Multiobjective quantum-inspired evolutionary algorithm (MQEA) employs Q-bit individuals, which are updated using rotation gate by referring to nondominated solutions in an archive. In this way, a population can quickly converge to the Pareto optimal solution set. To obtain the specific solutions based on user's preference in the population, MQEA with preference-based selection (MQEA-PS) is developed. In this paper, an improved version of MQEA-PS, MQEA-PS2, is proposed, where global population is sorted and divided into groups, upper half of individuals in each group are selected by global evaluation, and selected solutions are globally migrated. The global evaluation of nondominated solutions is performed by the fuzzy integral of partial evaluation with respect to the fuzzy measures, where the partial evaluation value is obtained from a normalized objective function value. To demonstrate the effectiveness of the proposed MQEA-PS2, comparisons with MQEA and MQEA-PS are carried out for DTLZ functions.