Crisp-set (csQCA), fuzzy-set (fsQCA) and multi-value Qualitative Comparative Analysis (mvQCA) have emerged as distinct variants of QCA, with the latter still being widely regarded as a less sophisticated technique of doubtful set-theoretic status. Textbooks on configurational comparative methodology have also generally emphasized differences rather than commonalities between these variants. This article has two objectives, both of which focus on commonalities. First, but secondary in importance, it demonstrates that all set types associated with each QCA variant can be combined within the same analysis. By implication, it also argues that the prevailing skepticism against mvQCA has no methodological foundation. And second, but primary in importance, it introduces the concept of the multivalent fuzzy set. This set type forms the basis of generalized-set Qualitative Comparative Analysis (gsQCA), an approach that integrates the features peculiar to mvQCA and fsQCA into a single framework while retaining routine truth table construction and Boolean minimization procedures. Under the concept of the multivalent fuzzy set, all existing QCA variants become special cases of gsQCA.
