Organizations make use of project management methodologies, which provide an effective manner to achieve managerial goals, maintain the strength of the companies in increasing competition. Efficiency in planning, budgeting, and scheduling are provided so that high quality outputs are obtained through these processes. Agile project management methodology, which has been emerged from unpredictability of customer requirements and changeable business environment, is apt to cope with the failures of traditional project management tools. Besides, lean six-sigma project management methodology has become a combination of lean and six-sigma, which were opponent methodologies previously. This paper aims to determine the most suitable outsourcing provider alternative by presenting a novel cognitive maps-based intuitionistic fuzzy decision making procedure. Interrelationships among evaluation criteria are weighted employing intuitionistic fuzzy cognitive map technique because of the causal links among evaluation criteria, vagueness, fuzziness, and hesitation in data. Moreover, the most appropriate provider alternative for both agile and lean six-sigma project management methodologies is identified by utilizing intuitionistic fuzzy TOPSIS method, which aims for minimizing the closeness to the ideal solution while maximizing the distance from the anti-ideal solution in hesitative environment. The case study is carried out in a bank that performs in Turkish banking sector.