Summary: In this paper, a new class of bi-cooperative games with fuzzy bi-coalitions is proposed in multilinear extension form. The extension is shown to be unique. The solution concept discussed in [S. Borkotokey and P. Sarmah, Fuzzy Sets Syst. 198, 46–58 (2012; Zbl 1251.91009)] is investigated and characterized for this class of games.