Measuring Polarization: A Fuzzy Set Theoretical Approach

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Abstract

The measurement of polarization has been studied over the last thirty years. Despite the different applied approaches, since polariza- tion concept is complex, we find a lack of consensus about how it should be measured. This paper proposes a new approach to the measurement of the polarization phenomenon based on fuzzy set. Fuzzy approach pro- vides a new perspective whose elements admit degrees of membership. Since reality is not black and white, a polarization measure should in- clude this key characteristic. For this purpose we analyze polarization metric properties and develop a new risk of polarization measure using aggregation operators and overlapping functions. We simulate a sample of N = 391315 cases across a 5-likert-scale with different distributions to test our measure. Other polarization measures were applied to compare situations where fuzzy set approach offers different results, where mem- bership functions have proved to play an essential role in the measure- ment. Finally, we want to highlight the new and potential contribution of fuzzy set approach to the polarization measurement which opens a new field to research on.

Authors

• Juan-Antonio Guevara, University Complutense of Madrid

• Jose Manuel Robles