In integral geometry, It is well known that the chord integral $I_q(K)$ is the Riesz potential of characteristic function of convex body $K$, for $q>1$,. In the case of $0<q<1$, we discover the new relationship between fractional perimeter and chord integral $I_q(K)$, which gives the representation formula of  $I_q(K)$ in the sense of Riesz potential. Under a pioneer work in integral geometry, Lutwak, Xi, Yang, and Zhang (CPAM 2024) established recently the variational formula for chord integral $I_q(K)$, for $q>0$, and defined the $q$-th chord measure. Meanwhile, they provided sufficient and necessary conditions for the existence of a solution to the chord Minkowski problem, for $q>0$, and sufficient conditions to solve the symmetric case of the chord log-Minkowski problem when $1\leq q \leq n+1$. Based on their work, we solve the symmetric case of chord log-Minkowski problem under a sufficient condition for $0<q<1$. Meanwhile, we solve the chord log-Minkowski problem when $0<q<1$, without symmetry assumptions. The talk is based on my work which have been published in Adv. Math. and Proc. AMS. in 2023