Outsourcing is the transfer of a business process that has been traditionally operated and managed internally to external service providers. In order to reduce costs and improve their core competitiveness, many companies tend to choose the outsourcing of some services. The problem of this type belongs to multicriteria decision making. The imprecision in this problem may arise from the nature of the characteristics of the candidates for the outsourcing service providers, which can be unavailable or indeterminate. It may also be derived from the inability of the experts to formulate a precise evaluation. Intuitionistic fuzzy sets (IFSs) are the stronger tool for dealing with uncertain data than fuzzy ones because, unlike them, they have a degree of hesitancy.Here, we will formulate an intuitionistic fuzzy generalized optimal outsoursing problem and an algorithm for selection the most effective outsourcing service providers is proposed using the consepts of index matrices (IMs) and intuitionistic fuzzy logic. The proposed decision model takes the ratings of the experts and the weighting factors of the evaluation criteria according to their priorities for the outsourcing services into consideration. The main contributions of the paper are: its proposition for intuitionistic fuzzy approach for selecting the most suitable candidates for outsourcing providers using the concept of IMs on the one hand, and its application for the outsourcing problem of a refinery.