We propose to use fuzzy context-free grammars for the analysis of DNA sequences by using the Cocke-Younger-Kasami algorithm to estimate membership grades of a DNA sequence against the language of a fuzzy grammar. As a first example of the application of the proposed method we prove that is possible to determine a fuzzy grammar of a prototype DNA sequence and then found the membership grade of any arbitrary sequence against the specific pattern. As a second example, we formulate a fuzzy grammar from an alignment of promoters by a logo sequence of Escherichia Coli K12 then show how the proposed method can be used for the discovery of regulatory motifs.