Uncertainty measures for general type-2 fuzzy sets

Five uncertainty measures have previously been defined for interval type-2 fuzzy sets (IT2 FSs), namely centroid, cardinality, fuzziness, variance and skewness. Based on a recently developed α-plane representation technique, this paper generalizes these definitions to general T2 FSs and, more importantly, derives a unified strategy for computing all different uncertainty measures with low complexity. The uncertainty measures of T2 FSs with different shaped Footprints of Uncertainty (FOU) and different triangular secondary membership functions are computed and are given as examples.

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