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The theory of Intuitionistic Fuzzy Sets (IFSs) is well suitable to deal with vagueness and hesitancy. In the present communication, a new parametric R-norm fuzzy entropy of type ‘α’ is proposed with the proof of validity. The intuitionistic fuzzy entropy is useful to represent the decision information in the process of decision making since it is characterized by the degree of satisfiability, degree of non-satisfiability and hesitancy degree. Based on the proposed R-norm fuzzy entropy of type ‘α’, a new decision making method of a Multi-Attribute Decision Making problem (MADM) has been introduced. In case of attribute weights, two cases (one with completely unknown attribute weights and other with partially known attribute weights) are discussed. The method is illustrated with the help of suitable examples.