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We explore the constraints on cosmological parameters in interacting dark energy (IDE) models described by energy transfer rates $Q = βH ρ_{\rm de}$ and $Q = βH ρ_{\rm c}$, using simulated gravitational-wave (GW) bright siren data from pulsar timing arrays (PTAs) and the Planck 2018 cosmic microwave background (CMB) data. In particular, we simulate a future PTA observation in the FAST/SKA era with 20 millisecond pulsars (MSPs), each having 20\,ns white noise over a 10-year observation span, and demonstrate that this mock dataset significantly improves the constraint precision of key cosmological parameters such as the Hubble constant $H_0$, matter density $Ω_m$, and the coupling parameter $β$. For the IDE model $Q = βH ρ_{\rm de}$, PTA data alone provides tighter constraints on these parameters than the CMB data alone, primarily due to the high sensitivity of GW standard sirens in probing the late universe. Combining PTA and CMB data further enhances the constraints by 43.6\% for $H_0$, 43.2\% for $Ω_m$, and 44.7\% for $β$, relative to using CMB data alone. In contrast, for $Q = βH ρ_{\rm c}$, the CMB data alone constrains $β$ more tightly than the PTA data, due to the stronger impact of this interaction in the early universe. Nevertheless, the PTA+\,CMB combination still yields improvements of 13.3\% for $H_0$, 22.7\% for $Ω_m$, and 18.2\% for $β$. Increasing the number of MSPs in the PTA further tightens all parameter constraints in both IDE models. Our results highlight the great potential of future PTA observations for significantly improving cosmological parameter estimation in IDE models, offering critical insights into the nature of dark energy and its interaction with dark matter.