The Choice between Crisp and Fuzzy Sets in Qualitative Comparative Analysis and the Ambiguous Consequences for Finding Consistent Set Relations

Empirical researchers using qualitative comparative analysis (QCA) can work with crisp, multivalue, and fuzzy sets. The relative advantages of crisp and multivalue sets have been discussed in the QCA literature. There has been little reflection on the more frequent decision between crisp and fuzzy sets for which there often is no theoretical guidance. A review shows that researchers often prefer fuzzy over crisp sets, sometimes because they contain more information. This meets with the argument that fuzzy sets produce more conservative consistency measures and constitute tougher tests. In my article, I demonstrate analytically and with data from published QCA studies that the relationship between crisp sets, fuzzy sets, and the consistency score is ambiguous. It depends on the distribution of cases whether the consistency value is more or less conservative for fuzzy sets than for crisp sets. I outline the implications of the ambiguous relationship for empirical research.