A new similarity measure for interval type-2 fuzzy sets: Application in fuzzy risk analysis

Abstract

Here, we present a fuzzy risk analysis method based on a new similarity measure of interval type-2 fuzzy sets (IT2-FSs). First, we present a new similarity measure for IT2-FSs. This measure considers features of IT2-FSs such as cardinality, height and distance. We establish some properties of the proposed similarity measure. We make an experiment to compare the experimental results obtained by the proposed method with the ones obtained by other existing similarity measures. The proposed method shows not to have the drawbacks of the existing methods. Applying the proposed method, we develop a fuzzy risk analysis approach extending the utility of fuzzy risk analysis methods in dealing with sophisticated problems. The factors used in the fuzzy risk analysis are the probability of failure, severity of loss, probability of failure detection and economic disbenefits of failure occurrence, features not being possible to use in existing interval type-2 fuzzy risk analysis methods.