•This study proposes a set of attributes to access sustainable solid waste management performance in Vietnam.•Fuzzy DEMATEL is to handle the interrelationships and ANP is to build the hierarchical structure to acquire the aspects and criteria weights.•Sustainable solid waste management requires the leadership of politics to drive stakeholders’ participations and social impacts.•Population growth and migration, institutional settings, waste recycling and energy recovery, households, and private contractors are critical for improvement. This study contributes to building a valid hierarchical sustainable solid waste management (SSWM) attribute set with qualitative information, which is a complicated and ambiguous problem with uncertainties. Few studies have provided qualitative information and have addressed the interrelationships and interdependencies among the hierarchical SSWM attributes. SSWM has recently become a difficult problem to solve due to urbanization, inequality, and economic growth. This study aims to propose an SSWM attribute set and identify a causal model through linguistic preferences by using a fuzzy decision-making trial and evaluation laboratory approach to simultaneously handle the uncertainty and the interrelationships. The analytic network process is used to develop the hierarchical structure to weigh the aspects and criteria. Qualitative information is transformed into crisp and comparable values to examine the causal relationships between attributes and confirm the consistency between the theoretical structure and industry phenomena. The results indicate that policy and regulations, stakeholder participation, and social impacts play essential roles in these causal interrelationships. Political leadership in SSWM is required to drive stakeholder participation and achieve social impacts. Population growth and migration, institutional settings, waste recycling and energy recovery, households, and private contractors are the main aspects involved in improving SSWM in Vietnam.