Crisp Set vs. Fuzzy Set Qualitative Comparative Analysis, Technical Differences, and Much More

Abstract

The idea of a mathematical formalization of logic that dates back to antiquity was only formalized in the 19th century by Charles Boole who proposed a binary system or clear sets. Although the fuzzy set theory is sometimes considered as a simple extension of Boolean algebra, the practical consequences for social science research are fundamental. The QCA has progressively seen the emergence of five increasingly sophisticated variants, the two main ones being the csQCA and the fsQCA. Is what opposes the crisp set qualitative comparative analysis (csQCA) to the fuzzy set qualitative comparative analysis (fsQCA) simply a technical improvement? The answer will be no; beyond different technical tools, there is a paradigm shift affecting in depth the research including epistemological choices, either explicit or implicit. In addition, part of these differences, which at first glance seem essentially methodological, are in fact partly due to a socio-cultural environment and religious values linked to the representation of the world, which is only rarely conscious.