  We report the joint analysis of single-dish and interferometric observations
of the Sunyaev-Zeldovich (SZ) effect from the galaxy cluster RX J1347.5-1145.
We have developed a parametric fitting procedure that uses native imaging and
visibility data, and tested it using the rich data sets from ALMA, Bolocam, and
Planck available for this object. RX J1347.5-1145 is a very hot and luminous
cluster showing signatures of a merger. Previous X-ray-motivated SZ studies
have highlighted the presence of an excess SZ signal south-east of the X-ray
peak, which was generally interpreted as a strong, shock-induced pressure
perturbation. Our model, when centred at the X-ray peak, confirms this.
However, the presence of two almost equally bright giant elliptical galaxies
separated by $\sim100\;{\rm kpc}$ makes the choice of the cluster centre
ambiguous, and allows for considerable freedom in modelling the structure of
the galaxy cluster. For instance, we have shown that the SZ signal can be
well-described by a single smooth ellipsoidal generalized Navarro-Frenk-White
profile, where the best-fitting centroid is located between the two brightest
cluster galaxies. This leads to a considerably weaker excess SZ signal from the
south-eastern substructure. Further, the most prominent features seen in the
X-ray can be explained as predominantly isobaric structures, alleviating the
need for highly supersonic velocities, although overpressurized regions
associated with the moving subhaloes are still present in our model.
