Previous fuzzy data envelopment analysis (FDEA) models separately solving for the lower and upper-bound efficiency frontiers under a specific a-cut level may lead to inconsistent efficiency rankings, unreasonable efficiency scores, and cumbersome slack computations. To rectify such shortcomings, this paper proposes two novel integrated fuzzy data envelopment analysis (IFDEA) models wherein both efficiency frontiers are incorporated into a single modelling formulation in ways that the slack values for lower- and upper-bound input/output variables are determined simultaneously. A numerical example shows that the proposed IFDEA models are more generalised and with greater simplicity than an existent FDEA model. A case study further demonstrates that the proposed IFDEA models can satisfactorily assess the relative efficiency for bus transport companies provided that a portion of the variables are measured qualitatively with vagueness (passenger satisfaction in this study).