Inspired by the recent investigations, a general framework for a class of $(\eta, \rho,\theta)$-invex $n$-set functions of higher order $r\geq 1$ is introduced, and then some optimality conditions for multiobjective fractional programming on the generalized $(\eta,\rho,\theta)$-invexity are established. The obtained results are general in nature and unify various results on fractional subset programming in the literature.