Using Web services to assess data in a distributed configuration, apart from different hardware and software platforms for employing standard criteria, is practical because of development in the Internet and network infrastructure. Distributed applications can transfer data using web services. Trust is the main criterion to select the appropriate web service. Neuro-fuzzy systems including clustering are applied to assess the trust of single web services. This paper considers nine criteria including quality of service, subjective perspectives, user preference, credibility of raters, objective perspectives, dynamic computing, bootstrapping, independency and security. To obtain a neuro-fuzzy system with high prediction accuracy, the paper considers eight neuro-fuzzy membership functions (i.e., trapmf, gbellmf, trimf, gaussmf, dsigmf, psigmf, gauss2mf, pimf) using the k-means clustering. Also, to increase the speed and reduce the fuzzy rules, a three-level neuro-fuzzy system (13 neuro-fuzzy) is investigated. The main target of this paper is evaluating the trust of single web services using the nine aforementioned criteria, as web services selection is a main issue which is still absorbing researchers to conduct research works on this field and analyze it. Ultimately, the results show reasonable root mean square error (RMSE) amount, precision value, recall value, and F-score value. In comparison to previous research works, this study obtained the lower amounts of errors and presents the more accurate trust of single web services.