of different classes of $\gamma$-ray blazar candidates. Then we describe our new association procedure.

The [[*WGS*]{}]{} parametrization {#sec:parameter}
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In Paper II, we found that $\gamma$-ray emitting blazars (i.e., those in the 2FB sample) cover a narrow region in the 3D color space built with the [[*WISE*]{}]{} magnitudes delineating the so-called [[*WISE*]{}]{} Gamma-ray blazar Strip ([[*WGS*]{}]{}).

In Paper III, using the 2FB sample, we presented the parametrization of the [[*WGS*]{}]{}  based on the [*strip parameter*]{} $s$. This parameter, ranging between 0 and 1, provides a measure of the distance between the [[*WGS*]{}]{} and the location of a [[*WISE*]{}]{} source in the three dimensional IR color parameter space. For example, sources with high values of $s$ (e.g., $\geq$ 0.50) are consistent with the [[*WGS*]{}]{}. We also distinguished between [[*WISE*]{}]{} sources that lie in the subregion of the [[*WGS*]{}]{}occupied by the BZBs and BZQs using the $s_b$ and $s_q$ parameters separately (Paper III).

The IR color space has been built using the archival data available in the 2011 [[*WISE*]{}]{} Preliminary Data Release, in four different bands centered at 3.4, 4.6, 12, and 22 $\mu$m with an angular resolution of 6.1, 6.4, 6.5 & 12.0$^{\prime\prime}$, respectively and achieving 5$\sigma$ point source sensitivities of 