Uncertainty degree of interval type-2 fuzzy sets and its application to thermal comfort modelling

Interval type-2 fuzzy sets (IT2 FSs) can model and cope with the uncertainties existing in the real-world applications. There exist several uncertainty measures for IT2 FSs, such as centroid, fuzziness, cardinality, variance and skewness. But, for most of such measures, there is no closed-form equations to compute them, which limits the application of these uncertainty measures in constructing IT2 FS models from uncertain interval end-points data. To tackle this problem, in this paper, we define a new concept - uncertainty degree to measure the IT2 FSs' ability to model the uncertainties. Closed-form equations of the uncertainty degree for different kinds of IT2 FSs are given. Based on the proposed concept, a new method for constructing IT2 FSs model of the thermal comfort is also presented. This application demonstrates the usefulness of the proposed concept on modelling the uncertainties contained in the uncertain survey data.