In this paper we deal with the problem of extending Zadeh's operators on fuzzy sets (FSs) to interval-valued (IVFSs), set-valued (SVFSs) and type-2 (T2FSs) fuzzy sets. Namely, it is known that seeing FSs as SVFSs, or T2FSs, whose membership degrees are singletons is not order-preserving. We then describe a family of lattice embeddings from FSs to SVFSs. Alternatively, if the former singleton vi...

Type-2 fuzzy sets and complex fuzzy sets are both three dimensional extensions of type-1 fuzzy sets. Complex fuzzy sets come in two forms, the standard form, postulated in 2002 by Ramot et al., and the 2011 innovation of pure complex fuzzy sets, proposed by Tamir et al.. In this paper we compare and contrast both forms of complex fuzzy set with type-2 fuzzy sets, as regards their rationales, ap...

This paper is an investigation of the automorphisms of the algebra of truth values of type-2 fuzzy sets. This algebra contains isomorphic copies of the truth value algebras of type-1 and of interval-valued fuzzy sets. It is shown that these subalgebras are characteristic; that is, are carried onto themselves by automorphisms of the containing algebra of truth values of fuzzy sets. Some other re...

In support of reasoning with sparse rule bases, fuzzy rule interpolation (FRI) offers a helpful inference mechanism for deriving an approximate conclusion when a given observation has no overlap with any rule in the existing rule base. One of the recent and popular FRI approaches is the scale and move transformation-based rule interpolation, known as T-FRI in the literature. It supports both in...

In the traditional fuzzy logic, the expert’s degree of certainty in a statement is described either by a number from the interval [0, 1] or by a subinterval of such an interval. To adequately describe the opinion of several experts, researchers proposed to use a union of the corresponding sets – which is, in general, more complex than an interval. In this paper, we prove that for such set-value...

AND ITS APPLICATION by YU QIU Under the Direction of Yanqing Zhang ABSTRACT In recent years, the type-2 fuzzy sets theory has been used to model and minimize the effects of uncertainties in rule-base fuzzy logic system. In order to make the type-2 fuzzy logic system reasonable and reliable, a new simple and novel statistical method to decide interval-valued fuzzy membership functions and a new ...

Whether a rule-based interval type-2 fuzzy system has the ability to approximate any continuous multivariate function arbitrarily well is a fundamentally important question for fuzzy control and modeling. The only approximation results available are the preliminary ones that we previously obtained. They state that two general classes of the interval T2 fuzzy systems, one for the Mamdani type an...