With respect to multiple criteria group decision making problems with conflicting and non-commensurable criteria, it is generally difficult to find an alternative that meets all the criteria simultaneously. By extending the fuzzy VIKOR method, this study provides a rational and systematic process for developing the best alternative and compromise solution under the interval-valued intuitionistic fuzzy environment. Furthermore, a fuzzy cross-entropy approach is proposed to state the discrimination measure between optional and optimal interval-valued intuitionistic fuzzy numbers. Finally, to expatiate on the practical value of the method proposed, an illustrative example is presented to demonstrate its practicality and effectiveness over existing TOPSIS method.