Type-2 fuzzy sets made simple
Jerry M. Mendel,Robert John +1 more
TLDR
Establishing a small set of terms that let us easily communicate about type-2 fuzzy sets and also let us define such sets very precisely, and presenting a new representation for type- 2 fuzzy sets, and using this new representation to derive formulas for union, intersection and complement of type-1 fuzzy sets without having to use the Extension Principle.Abstract:
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 us define such sets very precisely, (2) presenting a new representation for type-2 fuzzy sets, and (3) using this new representation to derive formulas for union, intersection and complement of type-2 fuzzy sets without having to use the Extension Principle.read more
Citations
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Journal ArticleDOI
Interval Type-2 Fuzzy Logic Systems Made Simple
TL;DR: This paper demonstrates that it is unnecessary to take the route from general T2 FS to IT2 FS, and that all of the results that are needed to implement an IT2 FLS can be obtained using T1 FS mathematics.
Journal ArticleDOI
A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots
TL;DR: A novel reactive control architecture for autonomous mobile robots that is based ontype-2 FLC to implement the basic navigation behaviors and the coordination between these behaviors to produce a type-2 hierarchical FLC is presented.
Journal ArticleDOI
Pythagorean Membership Grades, Complex Numbers, and Decision Making
Ronald R. Yager,Ali M. Abbasov +1 more
TL;DR: It is shown that Pythagorean membership grades are a subclass of complex numbers called Π‐i numbers, and the use of the geometric mean and ordered weighted geometric operator for aggregating criteria satisfaction is looked at.
Book
Body sensor networks
TL;DR: The aim of the BSN is to provide a truly personalised monitoring platform that is pervasive, intelligent, and effective in patients with chronic diseases such as heart disease.
Journal ArticleDOI
Type-2 fuzzy sets and systems: an overview
TL;DR: This paper provides an introduction to and an overview of type-2 fuzzy sets (T2 FS) and systems by answering the following questions: What is a T2 FS and how is it different from a T1 FS.
References
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Journal ArticleDOI
The concept of a linguistic variable and its application to approximate reasoning—II☆
TL;DR: Much of what constitutes the core of scientific knowledge may be regarded as a reservoir of concepts and techniques which can be drawn upon to construct mathematical models of various types of systems and thereby yield quantitative information concerning their behavior.
Book
Fuzzy Sets and Systems: Theory and Applications
Didier Dubois,Henri Prade +1 more
TL;DR: This book effectively constitutes a detailed annotated bibliography in quasitextbook style of the some thousand contributions deemed by Messrs. Dubois and Prade to belong to the area of fuzzy set theory and its applications or interactions in a wide spectrum of scientific disciplines.
Book
Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions
TL;DR: This chapter discusses Type-2 Fuzzy Sets, a New Direction for FLSs, and Relations and Compositions on different Product Spaces on Different Product Spaces, as well as operations on and Properties of Type-1 Non-Singleton Type- 2 FuzzY Sets.
Journal ArticleDOI
Operations on fuzzy numbers
Didier Dubois,Henri Prade +1 more
TL;DR: The usual algebraic operations on real numbers are extended to fuzzy numbers by the use of a fuzzification principle, and the practical use of fuzzified operations is shown to be easy, requiring no more computation than when dealing with error intervals in classic tolerance analysis.
Journal ArticleDOI
Interval type-2 fuzzy logic systems: theory and design
Qilian Liang,Jerry M. Mendel +1 more
TL;DR: 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 is proposed.