A novel decision support framework has been proposed herein to solve supplier selection problems by considering green as well as resiliency criteria, simultaneously. An expert team involving a finite number of Decision-Makers (DMs) is to be employed to obtain degree of importance of each of the evaluation criteria and also to assign an appropriate rating for each supplier alternative with respect to the criteria. Since subjective human judgment often bears some sort of ambiguity as well as vagueness, application of fuzzy set theory can be recommended in this context. The present work represents a dominance based decision support system in the light of fuzzy set theory which is basically a simplified version of TODIM and PROMETHEE. It explores dominance between two alternatives with respect to a particular criterion, based on which a global dominance measure is computed to facilitate ranking order of candidate suppliers. The approach proposed in this research seems straightforward which can exclude complex and tedious computational steps of TODIM as well as PROMETHEE. Application potential of the proposed dominance based fuzzy decision-making approach has been compared to that of Fuzzy-TOPSIS and Fuzzy-VIKOR. Good agreement has been observed. In addition to this, the concept of a unique performance index i.e. ‘g-resilient’ (also called ‘ecosilient’) index has been introduced to help in assessing suppliers’ overall performance extent. The work has also been extended to identify the ill (poor)-performing areas in which suppliers are lagging and seek further improvement towards enhancing g-resilient performance level.