As a critical component of sustainable development, a transportation system should be designed such that it has a positive impact on the economic, environmental, and social sustainability of the served region. In response, this study introduces the concept of passenger dissatisfaction with additional walking and waiting as an indicator of social sustainability and uses the concept while optimizing the transit network for economic, environmental, and social perfectives. Due to a lack of knowledge about the actual value of different passenger dissatisfaction levels and uncertainty in demand, a multi-objective robust possibilistic programming approach (RPP⁎) is proposed and solved by using an interactive fuzzy programming approach. Different from other robust possibilistic approaches, RPP⁎ optimizes not only the mean of the objective function and chance constraint violations but also the risk value inherited by uncertain parameters through considering the absolute deviation of the objective function. Both the advantage of RPP⁎ versus the deterministic model and its superiority against several robust possibilistic approaches are demonstrated in the numerical studies. Furthermore, the outcomes of the numerical study demonstrate that the transportation network should be designed in a decentralized way as the risk coefficients, i.e., risk-taking attitude, increase.