Abstract
Type-2 fuzzy sets (T2 FSs) have been shown to manage uncertainty more effectively than type-1 fuzzy sets (T1 FSs) in several areas of engineering. However, computing with T2 FSs can require an undesirably large amount of computations since it involves numerous embedded T2 FSs. To reduce the complexity, interval type-2 fuzzy sets (IT2 FSs) can be used, since the secondary memberships are all equal to one. In this chapter, three novel interval type-2 fuzzy membership function (IT2 FMF) generation methods are proposed. The methods are based on heuristics, histograms, and interval type-2 fuzzy C-means (IT2 FCM). For each method, the footprint of uncertainty (FOU) is only required to be obtained, since the FOU can completely describe an IT2 FMF. The performance of the methods is evaluated by applying them to back-propagation neural networks (BPNNs). Experimental results for several data sets are given to show the effectiveness of the proposed membership assignments.
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