  In this paper, we introduce a new type of Finsler metrics, called
$(\alpha_1,\alpha_2)$-metrics. We define the notion of the good datum of a
homogeneous $(\alpha_1,\alpha_2)$-metric and use that to study the geometric
properties. In particular, we give a formula of the S-curvature and deduce a
condition for the S-curvature to be vanishing identically. Moreover, we
consider the restrictive Clifford-Wolf homogeneity of left invariant
$(\alpha_1,\alpha_2)$-metrics on compact connected simple Lie groups. We prove
that, in some special cases, a restrictively Clifford-Wolf homogeneous
$(\alpha_1,\alpha_2)$-metric must be Riemannian. An unexpected interesting
observation contained in the proof reveals the fact that the S-curvature may
play an important role in the study of Clifford-Wolf homogeneity in Finsler
geometry.
