Chapter 5 : Qualitative Comparative Analysis Using Fuzzy Sets ( fsQCA ) Forthcoming in Benoit

One apparent limitation of the truth table approach is that it is designed for causal conditions that are simple presence/absence dichotomies (i.e., Boolean or "crisp" sets-chapter 3) or multichotomies (MVQCA--chapter 4). Many of the causal conditions that interest social scientists, however, vary by level or degree. For example, while it is clear that some countries are democracies and some are not, there is a broad range of inbetween cases. These countries are not fully in the set of democracies, nor are they fully excluded from this set. Fortunately, there is a well-developed mathematical system for addressing partial membership in sets, fuzzy-set theory (Zadeh 1965). Section 1 of this chapter provides a brief introduction to the fuzzy-set approach, building on Ragin (2000). Fuzzy sets are especially powerful because they allow researchers to calibrate partial membership in sets using values in the interval between 0 (nonmembership) and 1 (full membership) without abandoning core set theoretic principles, for example, the subset relation. As Ragin (2000) demonstrates, the subset relation is central to the analysis of causal complexity. While fuzzy sets solve the problem of trying to force-fit cases into one of two categories (membership versus nonmembership in a set) or into one of three or more categories (mvQCA), they are not well suited for conventional truth table analysis. 1