In this paper, Sheffer stroke BG-algebra is given. After determining a fuzzy ideal of Sheffer stroke BG-algebra, some properties are presented. Then a fuzzy implicative and a sub-implicative ideals of a Sheffer stroke BG-algebra are described. Morever, an implicative Sheffer stroke BG-algebra and a medial Sheffer stroke BG-algebra are defined and it is expressed that every medial Sheffer stroke BG-algebra is an implicative Sheffer stroke BG-algebra. Also, a fuzzy (completely) closed ideal and a fuzzy p-ideal are determined. Finally, the relationships between these structures are show
