The goal of this contribution is to introduce and study the theory of L M -valued Ftransforms, which is essentially the manyvalued generalizations of the notion of latticevalued F -transforms. Further, we associate the concepts of L M -valued fuzzy rough sets with L M -valued F -transforms and obtain some interesting results. Moreover, we show that the notion of F -transforms studied earlier can be considered as the particular case of L M -valued F -transforms.