Fuzzy Logic. The first book of its kind, this text explains how all kinds of uncertainties can be handled within the framework of a common theory...
—Type-2 fuzzy sets let us model and minimize the effects of uncertainties in rule-base fuzzy logic systems. However, they are difficult to understand for a variety of reasons which we enunciate. In this paper, we strive to overcome the difficulties by: 1) establishing a small set of terms that let us easily communicate about type-2 fuzzy sets and also let… (More)
—In this paper, we present the theory and design of interval type-2 fuzzy logic systems (FLSs). We propose an efficient and simplified method to compute the input and antecedent operations for interval type-2 FLSs; one that is based on a general inference formula for them. We introduce the concept of upper and lower membership functions (MFs) and illustrate… (More)
—To date, because of the computational complexity of using a general type-2 fuzzy set (T2 FS) in a T2 fuzzy logic system (FLS), most people only use an interval T2 FS, the result being an interval T2 FLS (IT2 FLS). Unfortunately, there is a heavy educational burden even to using an IT2 FLS. This burden has to do with first having to learn general T2 FS… (More)
Fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions. Using the Stone-Weierstrass theorem, it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy. Based… (More)
There is an Errata to this tutorial that is on the next two pages. You may want to print it out before you begin reading this article.
In this paper, we discuss set operations on type-2 fuzzy sets (including join and meet under minimum=product t-norm), algebraic operations, properties of membership grades of type-2 sets, and type-2 relations and their compositions. All this is needed to implement a type-2 fuzzy logic system (FLS).
—This paper presents a very practical type-2-fuzzistics methodology for obtaining interval type-2 fuzzy set (IT2 FS) models for words, one that is called an interval approach (IA). The basic idea of the IA is to collect interval endpoint data for a word from a group of subjects, map each subject's data interval into a prespec-ified type-1 (T1) person… (More)