Measuring social emergencies through fuzzy qualitative comparative analysis: a calibration framework using normalized general continuous linguistic variables

Social emergencies are complex societal phenomena characterized by nonlinear dynamics, multiple causality, and emergent properties that cannot be reduced to simple causal chains. Understanding the conditions that give rise to such emergencies requires analytical frameworks capable of capturing uncertainty, equifinality, and causal asymmetry. Fuzzy Qualitative Comparative Analysis (fsQCA) offers a set-theoretic approach well-suited to this challenge, combining the interpretive depth of qualitative methods with the rigor of formal logic. However, a central obstacle in its application is the calibration of fuzzy membership functions, which determines how raw social data are translated into degrees of set membership. This paper proposes a novel calibration framework based on the Normalized General Continuous Linguistic Variable (NGCLV), a flexible parametric function capable of taking increasing, decreasing, or convex forms by adjusting a single shape parameter. We introduce one direct calibration method—fitting membership functions to empirical data—and two indirect calibration methods based on partition and linguistic selection approaches. All three methods are demonstrated using a real-world dataset of health indicators across twenty countries, with Life Expectancy as the sociological outcome of interest. We further propose an optimization method that maximizes the joint consistency and coverage indices, automating the identification of the most explanatorily powerful causal configuration. Results show that NGCLVs improve calibration flexibility and semantic interpretability compared to conventional membership functions. The proposed framework advances the methodological toolkit available for sociological research involving small-to-medium case sets, complex causality, and the need to integrate expert knowledge with empirical data.