Description: The analysis of development of mathematical theory of making a decision is conducted in the conditions of vagueness. Advantages and lacks of theory of fuzzy sets are analysed. The presence of dynamic models, within the framework of which or during the use of which it is expedient to foresee possibility of change of type of functions of belonging of fuzzy sets by which in the conditions of vagueness some knowledges or phenomena are described, is grounded. The concept of dynamic fuzzy set the use of which expediently in such dynamic models is offered.
Keywords: vagueness, dynamic models, fuzzy sets