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Web services have become one of the most popular technologies of Web application. But the quality of Web services is not as stable as traditional software components' because of the uncertainty of network. Based on non-probability-set, the convex method is used to judge the range of performance affected by uncertain-but-bounded attributes. This method only requires the highest and lowest value of the uncertain attribute values and need not to know their probability distribution. This paper proposes the metric algorithm of the change of web service quality, and proposes the Web service decisionmaking algorithm based on the theory of multiple attributes decision by TOPSIS (technique for order preference by similarity to idea solution) in operations research.