In the present paper, the convexity of fuzzy sets is generalized 
based on conjunctive aggregation functions, 
and the degree of the non-convexity of fuzzy sets is considered 
as an application of the generalized convexity. 
Then, the properties of the generalized convexity of fuzzy sets, 
and the properties of the degree of the non-convexity of fuzzy sets with respect to operations 
are investigated.