Understanding societal preferences towards health is vital in public decisions on nancing health technologies. Thought experiments in which respondents choose between health states are used to understand the importance of individual criteria. Competing models of preference structure can be compared by their ability to explain empirical observations. One of the key challenges when constructing such models is that they have to aggregate preferences dened in multiple-criteria space. In the present paper, we test whether treating the impact of health worsening (dened using EQ-5D-5L descriptive system, i.e. decomposing health status in ve criteria) as a fuzzy concept can improve the model fit. To test if fuzzy approach to multiple-criteria preferences aggregation is valid, we compare a standard, crisp model (SM) with two models using fuzzy sets (JKL, previously proposed in the literature; and FMN introduced here). We nd FMN better than SM, and SM better than JKL. Anxiety/depression and pain/discomfort seem to weigh most in preferences. According to FMN, self-care and usual activities are associated with largest imprecision in preferences. The respondents are susceptible to framing eects when time unit is changed: e.g. measuring the duration in days results in short intervals mattering more than when expressed as weeks. We conclude that the fuzzy-based framework is promising, but requires careful work on the exact specication.