− In this paper, we introduce several types of fuzzy pairwise compactness and fuzzy pairwise compactness modulo a smooth ideal in smooth bitopological spaces by using the family of r(τi, τj)-fuzzy semi-open sets as cover. Several characterizations and some properties of these spacesare discussed. Preservation of fuzzy pairwise compactness modulo a smooth ideal by some types ofmappings is also investigated