There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Data Mining - Concepts and Techniques.

Data Mining Practical Machine Learning Tools and Techniques

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.

/pdf/type-2-fuzzy-sets-made-simple-3iyg95vkei.pdf

Type-2 fuzzy sets made simple

/pdf/a-break-in-the-clouds-towards-a-cloud-definition-svovsw1r5a.pdf

A Break in the Clouds: Towards a Cloud Definition

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

/pdf/interval-type-2-fuzzy-logic-systems-made-simple-as15zfz2h0.pdf

Interval Type-2 Fuzzy Logic Systems Made Simple

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

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

Robert John

Papers

Type-2 fuzzy sets made simple

Interval Type-2 Fuzzy Logic Systems Made Simple

Geometric Type-1 and Type-2 Fuzzy Logic Systems

Type-2 Fuzzy Logic: A Historical View

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