A novel decision support framework has been proposed herein to solve supplier selection problems by considering green as well as resiliency criteria, simultaneously. In this work subjectivity of evaluation criteria has been tackled by exploring fuzzy set theory. A dominance based approach has been conceptualized which is basically a simplified version of TODIM. Application potential of the proposed dominance based fuzzy decision making approach has been compared to that of fuzzy-TOPSIS, fuzzy-VIKOR and also fuzzy-TODIM. The concept of a unique performance index, i.e. “g-resilient” index has been introduced here to help in assessing suppliers’ performance and thereby selecting the best candidate. The work has also been extended to identify the areas in which suppliers are lagging; these seek further improvement towards g-resilient suppliers’ performance to be boosted up to the desired level.