  We propose the doubly $\kappa$-dependent Yang quantum phase space which
describes the generalization of $D = 4$ Yang model. We postulate that such
model is covariant under the generalized Born map, what permits to derive this
new model from the earlier proposed $\kappa$-Snyder model. Our model of $D=4$
relativistic Yang quantum phase space depends on five deformation parameters
which form two Born map-related dimensionful pairs: $(M,R)$ specifying the
standard Yang model and $(\kappa,\tilde{\kappa})$ characterizing the Born-dual
$\kappa$-dependence of quantum space-time and quantum fourmomenta sectors;
fifth parameter $\rho$ is dimensionless and Born-selfdual. In the last section,
we propose the Kaluza-Klein generalization of $D=4$ Yang model and the new
quantum Yang models described algebraically by quantum-deformed $\hat{o}(1,5)$
algebras.
