Abstract: The concept of inclusion degree of vague sets is applied to multi-criteria decision making in fuzzy environment.First,inclusion degree of vague sets is defined and a series of specific formulas of inclusion degree are presented by means of the norml implication operators.Some formulas of inclusion degree of fuzzy sets are generalized to vague sets by defining the cardinal number of vague sets.Then,we give multi-criteria fuzzy decision-making method based on inclusion degree of vague sets.Finally,we illustrate the effectiveness of the method proposed in this paper by an example.

Key words: multi-criteria fuzzy decision-making, vague sets, inclusion degree, normal implication, cardinal number