In this work we propose an approach of multi-criteria decision making (MCDM) using TOPSIS and VIKOR methods under interval-valued intuitionistic fuzzy (IVIF) sets and possibility theory. We are interested to study positive and negative ideal solutions to propose new formulas. Indeed, these solutions are presented with many formulas in literature [1, 2] which could cause ambiguity [3]. Due to the importance of possibility theory in resolution of many problems, we propose to use possibility measure for positive ideal solution and necessity measure for negative ideal solution under interval valued intuitionistic fuzzy sets. According to this, TOPSIS and VIKOR are modified to obtain new approaches. The latter are applied to an example from literature using IVIF data. This example permits to assess the investment projects problem for ranking different projects. The found results showed different solutions from that existing in literature which can give more choice to decision makers with additional information due to use of possibility measures.
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