Interval type-2 fuzzy set qualitative comparative analysis (IT2-fsQCA)

Fuzzy Set Qualitative Comparative Analysis (fsQCA) is a methodology for obtaining linguistic summarizations from data that are associated with cases. It seeks to establish logical connections between combinations of causal conditions and an outcome, the result being rules that summarize the sufficiency between subsets of all of the possible combinations of the causal conditions (or their complements) and the outcome. The rules are connected by the word OR to the output. Each rule is a possible path from the causal conditions to the outcome. FsQCA rules involve words that are modeled using type-1 fuzzy sets (T1 FSs). Unfortunately, once the T1 FS membership functions (MFs) have been chosen, all uncertainty about the words that are used in fsQCA disappears, because T1 MFs are totally precise. Interval type-2 FSs (IT2 FSs), on the other hand, are first-order uncertainty models for words. In this paper, we extend fsQCA to IT2 FSs. More specifically, we develop IT2-fsQCA by extending the steps of fsQCA from T1 FSs to IT2 FSs. In order to illustrate the application of IT2-f5QCA we consider Ragin´s Breakdown of Democracy example, which studies the effects of five causal conditions on the Breakdown of Democracy of 18 European countries between World Wars 1 and 2. We show results obtained for IT2-fsQCA and compare them with those obtained from fsQCA.