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QoS-based web service selection is an important aspect for achieving efficient operations for web service systems. The aim of web service selection is to select an appropriate concrete web service with the best quality of service (QoS) for each abstract web service in a workflow. One way to resolve this problem is to calculate the Pareto optimal solutions which have the better QoS values for some QoS attributes while having at least equivalent values for others. Although a lot of approaches can do that, they do not guarantee the result precision or have prohibitively large overhead. In this paper, we present an Advanced A-Fully Polynomial Time Approximation Scheme (A2-FPTAS) by the unequal local error bound to balance the precision and the overhead. Experimental results are presented to show the efficiency of this approach.