One of the most dramatic changes in information technology (IT) is the emergence of cloud services. Today, many software companies deliver their applications from a cloud system, which provides a valuable alternative for business buyers. Just like any other IT decision, the selecting proper cloud service provider contains various tangible and intangible criteria, which contain uncertainty and incomplete information. In this paper, selecting cloud service provider problem is modeled as a multi criteria decision-making problem, and a decision model involving seven criteria, 21 sub-criteria and four alternatives is proposed. The evaluations regarding the cloud alternatives are expressed as Pythagorean fuzzy sets. Pythagorean fuzzy sets are an extension of intuitionistic fuzzy sets, in which the sum of membership and non-membership degrees may be larger than one whereas their square sum is at most equal to 1. This provides a larger range for decision makers to assign membership and non-membership degrees to an element of a fuzzy set. Pythagorean fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method is used to rank the alternatives. The robustness of the decision model is checked using one-at-a-time sensitivity analysis.