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tokens: Collaboration XIV 2016b ); see Wen Wang ( 2017 ) for more details on the calculations of CMB (represented by the green contours in Figs 3 and 4 ). 2 We can see that when the observations of lensed GWEM systems are verified in the future, CMB constraints would benefit from having the constraints of lensed GWEM systems overlaid. 4 SUMMARY AND DISCUSSION Although the constraints on cosmological parameters have reached a high precision, all of the constraints so far have relied on EM observations alone. New multimessenger signals exploiting different emission channels are worth exploring in cosmology. Recently, Liao etal. ( 2017 ) proposed that future time-delay measurements of strongly lensed GW signals and their EM counterparts have great potential to infer cosmological parameters. Compared with the traditional approach of using strongly lensed quasar systems observed in the EM domain, the approach with lensed systems observed in both GW and EM windows has two advantages in constraining cosmological parameters. First, the time delays () between lensed images inferred from the GW signals would reach an extremely high accuracy (0.1s) from the detection pipeline, and such accurate measurements of would play an important role in boosting the development of precision cosmology. Secondly, with gravitationally lensed GWs and EM signals, the accuracy of lens modelling could be improved to some extent, leading to better constraints on cosmological parameters. In the EM window, Paraficz Hjorth ( 2009 ) suggested that the joint observations of the time delay () between lensed quasar images and the velocity dispersion () of the lensing galaxy are more effective to constrain cosmological parameters than or 2 separately. In this work, we apply the / 2 method, for the first time, to the strongly lensed systems observed in both GW and EM windows. We prove that both and / 2 from strongly lensed GWEM systems can serve as powerful cosmic rulers. From the comparison of the two different methods, we confirm that the / 2 method can provide tighter constraints on m than the method (i.e. using / 2 can make it easier to differentiate different cosmological models). Furthermore, we show that with a moderate sample size of 50, a constraint on the dark-energy equation of state w can be reached that is comparable to the 580 Union2.1 SNe Ia sample. Combining the and / 2 methods, it is possible to achieve higher accuracy in constraining w . The recent Advanced LIGO observations of binary black hole mergers GW150914 (Abbott etal. 2016a ), GW151226 (Abbott etal. 2016b ) and GW170104 (Abbott etal. 2017 ) have initiated the era of GW astronomy. Because of the high sensitivity, the planned third-generation GW detectors, such as the ET, could observe strongly lensed GWs. Recent works (Pirkowska etal. 2013 ; Biesiada etal. 2014 ; Ding etal. 2015 ) have carefully studied the prospects of observing strongly lensed GWs from merging double compact objects, which predicted that the ET