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 mathematics, and then specializing it to an IT2 FSs. In retrospect, we believe that requiring a person to use T2 FS mathematics represents a barrier to the use of an IT2 FLS. In this paper, we demonstrate 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. As such, this paper is a novel tutorial that makes an IT2 FLS much more accessible to all readers of this journal. We can now develop an IT2 FLS in a much more straightforward way

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Interval Type-2 Fuzzy Logic Systems Made Simple

Computer and Robot Vision Vol. 1, by R.M. Haralick and Linda G. Shapiro, Addison-Wesley, 1992, ISBN 0-201-10887-1.

Computer and Robot Vision

This paper provides an introduction to and an overview of type-2 fuzzy sets (T2 FS) and systems. It does this by answering the following questions: What is a T2 FS and how is it different from a T1 FS? Is there new terminology for a T2 FS? Are there important representations of a T2 FS and, if so, why are they important? How and why are T2 FSs used in a rule-based system? What are the detailed computations for an interval T2 fuzzy logic system (IT2 FLS) and are they easy to understand? Is it possible to have an IT2 FLS without type reduction? How do we wrap this up and where can we go to learn more?

Type-2 fuzzy sets and systems: an overview

▶ Addresses the accessibility, usability, and, ultimately, acceptability of Information Society Technologies by anyone, anywhere, at anytime, and through any media and device. ▶ Focuses on theoretical, methodological, and empirical research, of both technological and non-technological nature. ▶ Features papers that report on theories, methods, tools, empirical results, reviews, case studies, and best-practice examples.

Universal access in the information society

Transfer learning aims to provide a framework to utilize previously-acquired knowledge to solve new but similar problems much more quickly and effectively. In contrast to classical machine learning methods, transfer learning methods exploit the knowledge accumulated from data in auxiliary domains to facilitate predictive modeling consisting of different data patterns in the current domain. To improve the performance of existing transfer learning methods and handle the knowledge transfer process in real-world systems, computational intelligence has recently been applied in transfer learning. This paper systematically examines computational intelligence-based transfer learning techniques and clusters related technique developments into four main categories: (a) neural network-based transfer learning; (b) Bayes-based transfer learning; (c) fuzzy transfer learning, and (d) applications of computational intelligence-based transfer learning. By providing state-of-the-art knowledge, this survey will directly support researchers and practice-based professionals to understand the developments in computational intelligence-based transfer learning research and applications.

/pdf/transfer-learning-using-computational-intelligence-4ew6undoyg.pdf

Transfer learning using computational intelligence

This paper presents a novel approach to the representation of type-1 and type-2 fuzzy sets utilising computational geometry. To achieve this our approach borrows ideas from the field of computational geometry and applies these techniques in the novel setting of fuzzy logic. We provide new algorithms for various operations on type-1 and type-2 fuzzy sets and for defuzzification. Results of experiments indicate that this approach reduces the execution speed of these operations

Geometric Type-1 and Type-2 Fuzzy Logic Systems

Type-2 fuzzy logic offers an opportunity to model levels of uncertainty with which traditional fuzzy logic (type-1) struggles. This article provides a historical perspective of the development of type-2 fuzzy logic with a retrospective review of important developments in the field. We discuss key questions about the technology such as - when should type-2 systems be used? and why has it taken so long for this technology to emerge? The article concludes by highlighting areas where, we believe, type-2 fuzzy logic will have a significant role to play in the future

Type-2 Fuzzy Logic: A Historical View

Construction of interval type-2 fuzzy set models is the first step in the perceptual computer, which is an implementation of computing with words. The interval approach (IA) has, so far, been the only systematic method to construct such models from data intervals that are collected from a survey. However, as pointed out in this paper, it has some limitations, and its performance can be further improved. This paper proposes an enhanced interval approach (EIA) and demonstrates its performance on data that are collected from a web survey. The data part of the EIA has more strict and reasonable tests than the IA, and the fuzzy set part of the EIA has an improved procedure to compute the lower membership function. We also perform a convergence analysis to answer two important questions: 1) Does the output interval type-2 fuzzy set from the EIA converge to a stable model as increasingly more data intervals are collected, and 2) if it converges, then how many data intervals are needed before the resulting interval type-2 fuzzy set is sufficiently similar to the model obtained from infinitely many data intervals? We show that the EIA converges in a mean-square sense, and generally, 30 data intervals seem to be a good compromise between cost and accuracy.

Enhanced Interval Approach for Encoding Words Into Interval Type-2 Fuzzy Sets and Its Convergence Analysis

http://www.cse.dmu.ac.uk/~chiclana/publications/A-INS-01(JUNE09).pdf

The collapsing method of defuzzification for discretised interval type-2 fuzzy sets

Generalized type-2 fuzzy logic systems cannot currently be used for practical problems because the amount of computation required to defuzzify a generalized type-2 fuzzy set is too large. This paper presents a new method for defuzzifing a type-2 fuzzy set. The new much faster technique is based on geometric representations and operations. The results of a real world example contained in this paper show this new approach to be over 200,000 times faster than type-reduction. We present a new method for assessing the accuracy of the membership function of a type-2 fuzzy set. This method is used to show that the new representation used by the defuzzifier is not detrimental to the accuracy of the set. We also discuss the differences between the new approach and type-reduction, identifying the origin of this massive improvement in execution speed.

Simon Coupland

Papers

Geometric Type-1 and Type-2 Fuzzy Logic Systems

Type-2 Fuzzy Logic: A Historical View

Enhanced Interval Approach for Encoding Words Into Interval Type-2 Fuzzy Sets and Its Convergence Analysis

The collapsing method of defuzzification for discretised interval type-2 fuzzy sets

A Fast Geometric Method for Defuzzification of Type-2 Fuzzy Sets