Waste management has become a serious problem in China, with households generating an increasing amount of waste. To tackle this problem, many city administrations have implemented regulations on household waste separation and are stepping up efforts to improve awareness. Moreover, the existence of individual interactions in social networks makes the cost of raising awareness highly uncertain. Therefore, this paper aims to describe the individual interactions based on dynamics of opinion spread method and build the incentive strategy model that is extended to three robust incentive strategy models based on various uncertain sets by robust optimization: Box-SO Model, Ellipsoid-SO Model and Box-Ellipsoid-SO Model. The simulation results indicated that a higher uncertain level parameter or a lower interaction threshold leads to lower public awareness, in which the Ellipsoid-SO Model has the best robustness with sacrificing 7.96% of the total awareness value, but the Box-Ellipsoid-SO Model loses 24.24%. Meanwhile, cost constraint has a direct effect on public awareness, and people with a high frequency of social interactions are key to improving public awareness of household waste separation. Additionally, the results have several management implications that are conducive to improving public awareness and behavior of household waste separation in social networks: (1) The fundamental premise of improving public waste separation behavior is to stimulate awareness; (2) Small-scale activities are more efficient than large-scale activities in improving pro-environment opinion; (3) Given the existence of opinion leaders, propaganda for residents should be pertinently targeted. • Social interactions of awareness on household waste separation are studied. • Incentive models with cost uncertainties are proposed to improve awareness. • Awareness values of robust models are lower than basic model due to uncertainty. • Ellipsoid-SO Model has best robustness with losing 7.96% of the total awareness. • Small-scale activities are more efficient to improve public awareness.