With respect to the limitations existed in methods for calculating entropy of intuitionistic fuzzy sets, a new
entropy for intuitionistic fuzzy sets is proposed and the result of this entropy is compared with other existing entropies.
For the intuitionistic linguistic fuzzy multi-criteria decision-making problem, in which the information on the weights of
criteria are incomplete, a linear fuzzy programming model based on intuitionistic fuzzy entropy is constructed to obtain the
criteria weights. Then, intuitionistic linguistic weighted arithmetic averaging operator is used to aggregate the intuitionistic
linguistic fuzzy information corresponding to each alternative, and the alternatives are ranked by the score function. Finally,
an illustrative example is given to verify the effectiveness and rationality of the developed approach.