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The formation and evolution of a planetary system are intrinsically linked to the evolution of the primordial accretion disk and its dust and gas content. A new class of pre-main sequence objects has been recently identified as pre-transitional disks. They present near-infrared excess coupled to a flux deficit at about 10 microns and a rising mid-infrared and far-infrared spectrum. These features suggest a disk structure with inner and outer dust components, separated by a dust-depleted region (or gap). This could be the result of particular planet formation mechanisms that occur during the disk evolution. We here report on the first interferometric observations of the disk around the Herbig Ae star HD 139614. Its infrared spectrum suggests a flared disk, and presents pre-transitional features, namely a substantial near-infrared excess accompanied by a dip around 6 microns and a rising mid-infrared part. In this framework, we performed a study of the spectral energy distribution (SED) and the mid-infrared VLTI/MIDI interferometric data to constrain the spatial structure of the inner dust disk region and assess its possibly multi-component structure. We based our work on a temperature-gradient disk model that includes dust opacity. While we could not reproduce the SED and interferometric visibilities with a one-component disk, a better agreement was obtained with a two-component disk model composed of an optically thin inner disk extending from 0.22 to 2.3 AU, a gap, and an outer temperature-gradient disk starting at 5.6 AU. Therefore, our modeling favors an extended and optically thin inner dust component and in principle rules out the possibility that the near-infrared excess originates only from a spatially confined region. Moreover, the outer disk is characterized by a very steep temperature profile and a temperature higher than 300 K at its inner edge. This suggests the existence of a warm component corresponding to a scenario where the inner edge of the outer disk is directly illuminated by the central star. This is an expected consequence of the presence of a gap, thus indicative of a "pre-transitional" structure. [ABSTRACT FROM AUTHOR]