This paper introduces a new methodology for solving Multi-Attribute Decision Making (MADM) problems under hesitant fuzzy environment. The uncertainty in Hesitant Fuzzy Elements (HFE) are derived by means of entropy. The resulting uncertainty is subsequently used in HFE to derive a single representative value (RV) of alternatives in each attribute. Our work transforms the RVs into their linguistic counterparts and then formulates a methodology for pairwise comparison of the alternatives via their linguistically defines RVs. The Eigen vector corresponding to maximum Eigen value of the pairwise comparison matrix prioritize the alternatives in each attribute. The priority vectors of the alternatives are aggregated to derive the weights of the attributes using Quadratic programming. The weighted aggregation of the attribute values provides the ranking of the alternatives in MADM. An algorithm is written to validate the procedure developed. The proposed methodology is compared with similar existing methods and the advantages of our method are presented. The robustness of our methodology is demonstrated through sensitivity analysis. To highlight the procedure a car purchasing problem is illustrated.