Trust is a fundamental concept that is critical in human decision processes in almost all domains, but of particular relevance in the domain of computer security. In many computer systems deployed today, trust is only modeled indirectly through a serious of formal rules and regulations describing when privileges are to be granted or revoked. Recently, research has been conducted into the area o...

In the classical image processing paradigm, the fundamental idea of image enhancement is to produce a new image such that it exposes information for analysis more than the original image. Fuzzy Logic methods are one of valuable and frequently used techniques among many other image enhancement approaches. In this work we demonstrate that a type-2 fuzzy logic system is able to perform image contr...

We introduce a type-2 fuzzy logic system (FLS), which can handle rule uncertainties. The implementation of this type-2 FLS involves the operations of fuzzification, inference, and output processing. We focus on “output processing,” which consists of type reduction and defuzzification. Type-reduction methods are extended versions of type-1 defuzzification methods. Type reduction captures more in...

In this paper we study two important concepts, i.e. the direct andthe inverse limit of hyperstructures associated with fuzzy sets of type 2, andshow that the direct and the inverse limit of hyperstructures associated withfuzzy sets of type 2 are also hyperstructures associated with fuzzy sets of type 2.

Type-2 fuzzy sets are growing in popularity as, for certain applications they model uncertainty and imprecision better than type1 fuzzy sets. However, type-2 fuzzy sets can be difficult to understand and explain. Recent work has introduced embedded type-2 fuzzy sets and the Representation Theorem which enable us to discuss type-2 fuzzy sets in a different way. In particular they allow for alter...

Recently there has been significant growth in research interest in type-2 fuzzy logic. Type-2 fuzzy logic is extension of type-1 (regular) fuzzy logic where the membership grade in a fuzzy set is itself measured as a fuzzy number. Much of this growth has only been concerned with type-2 interval fuzzy systems, a subset of type-2 fuzzy systems, where the membership grade of a fuzzy set is given a...

Image segmentation is an essential issue in image description and classification. Currently, in many real applications, segmentation is still mainly manual or strongly supervised by a human expert, which makes it irreproducible and deteriorating. Moreover, there are many uncertainties and vagueness in images, which crisp clustering and even Type-1 fuzzy clustering could not handle. Hence, Type-...

This chapter presents a new optimization method for clustering fuzzy data to generate Type-2 fuzzy system models. For this purpose, first, a new distance measure for calculating the (dis)similarity between fuzzy data is proposed. Then, based on the proposed distance measure, Fuzzy c-Mean (FCM) clustering algorithm is modified. Next, Xie-Beni cluster validity index is modified to be able to valu...