Bridging Crisp-Set Qualitative Comparative Analysis and Association Rule Mining: A Formal and Computational Integration

Acácio Dom Luís, Rafael Benítez () and María del Carmen Bas
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Acácio Dom Luís: Departamento de Matemáticas para la Economía y la Empresa, Facultad de Economía, Universidad de Valencia, Avda. Tarongers s/n, 46022 Valencia, Spain
Rafael Benítez: Departamento de Matemáticas para la Economía y la Empresa, Facultad de Economía, Universidad de Valencia, Avda. Tarongers s/n, 46022 Valencia, Spain
María del Carmen Bas: Departamento de Matemáticas para la Economía y la Empresa, Facultad de Economía, Universidad de Valencia, Avda. Tarongers s/n, 46022 Valencia, Spain

Mathematics, 2025, vol. 13, issue 12, 1-28

Abstract: In this paper, a novel mathematical formalization of Crisp-Set Qualitative Comparative Analysis (csQCA) that enables a rigorous connection with a specific class of association rule mining (ARM) problems is proposed. Although these two methodologies are frequently used to identify logical patterns in binary datasets, they originate from different traditions. While csQCA is rooted in set theory and Boolean logic and is primarily applied in the social sciences to model causal complexity, ARM originates from data mining and is widely used to discover frequent co-occurrences among items. In this study, we establish a formal mathematical equivalence between csQCA configurations and a subclass of association rules, including both positive and negative conditions. Moreover, we propose a minimization procedure for association rules that mirrors the Quine–McCluskey reduction method employed in csQCA. We demonstrate the consistency of the results obtained using both methodologies through two examples (a small-N study on internet shutdowns in Sub-Saharan Africa and a large-N analysis of immigration attitudes in Europe) and some numerical experiments. However, it is also clear that ARM offers improved scalability and robustness in high-dimensional contexts. Overall, these findings provide researchers with valuable theoretical and practical guidance when choosing between these approaches in qualitative data analysis.

Keywords: qualitative comparative analysis; association rule mining; Boolean logic; causal inference (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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