VIKOR method being one of the frequently used Multi-Criteria Decision Making (MCDM) methods, is based on the distances of alternatives to positive and negative ideal solutions, and presents compromising solutions. AHP is another MCDM method dividing the big problem into small and manageable problems through pairwise comparisons of criteria and alternatives. In these methods, linguistic assessments are generally preferred since exact numerical assignments of criteria values are really difficult and experts can not reflect the thoughts in their minds with crisp numbers. The fuzzy set theory captures the vagueness and impreciseness in these linguistic assessments successfully thorough fuzzy numbers. Circular intuitionistic fuzzy sets (C-IFS) are the latest extension of ordinary fuzzy sets, which was introduced by Atanassov . C-IFS help experts to define membership (belongingness) and nonmembership (unbelongingness) degrees by incorporating the uncertainty of these degrees. In this paper, an integrated C-IF AHP & CIF VIKOR methodology is developed and applied to a multi-expert supplier evaluation problem. The results obtained from the proposed methodology are compared with other methods, and a sensitivity analysis is performed as well.