The development of the web technologies and the increasing of available services have introduced the issue of the selection of the most appropriate service among a set of candidate web services. First of all, the services offering a given functionality are discovered. Then, the service section process assists users in choosing the services that better meets their preferences. These preferences are generally, expressed as potentially objective functions often conflicting. Most of existing works trying to select the best web services are based either on a single evaluation criterion or, at best, on the use of an aggregation function like weighted sum of several quantitative evaluation criteria, or the use of the Pareto optimality notion. The work presented here addresses these shortcomings by introducing a new optimality notion based on two tests: (i) concordance and (ii) discordance tests. It presents an efficient algorithm to select only the best services using the introduced optimality notion. Moreover, the proposed algorithm exhibits encouraging results as supported by a series of experiments.