Type-2 Fuzzy Alpha-cuts

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dc.contributor.author Hamrawi, Hussam
dc.date.accessioned 2011-08-16T09:10:02Z
dc.date.available 2011-08-16T09:10:02Z
dc.date.issued 2011
dc.identifier.uri http://hdl.handle.net/2086/5137
dc.description.abstract Systems that utilise type-2 fuzzy sets to handle uncertainty have not been implemented in real world applications unlike the astonishing number of applications involving standard fuzzy sets. The main reason behind this is the complex mathematical nature of type-2 fuzzy sets which is the source of two major problems. On one hand, it is difficult to mathematically manipulate type-2 fuzzy sets, and on the other, the computational cost of processing and performing operations using these sets is very high. Most of the current research carried out on type-2 fuzzy logic concentrates on finding mathematical means to overcome these obstacles. One way of accomplishing the first task is to develop a meaningful mathematical representation of type-2 fuzzy sets that allows functions and operations to be extended from well known mathematical forms to type-2 fuzzy sets. To this end, this thesis presents a novel alpha-cut representation theorem to be this meaningful mathematical representation. It is the decomposition of a type-2 fuzzy set in to a number of classical sets. The alpha-cut representation theorem is the main contribution of this thesis. This dissertation also presents a methodology to allow functions and operations to be extended directly from classical sets to type-2 fuzzy sets. A novel alpha-cut extension principle is presented in this thesis and used to define uncertainty measures and arithmetic operations for type-2 fuzzy sets. Throughout this investigation, a plethora of concepts and definitions have been developed for the first time in order to make the manipulation of type-2 fuzzy sets a simple and straight forward task. Worked examples are used to demonstrate the usefulness of these theorems and methods. Finally, the crisp alpha-cuts of this fundamental decomposition theorem are by definition independent of each other. This dissertation shows that operations on type-2 fuzzy sets using the alpha-cut extension principle can be processed in parallel. This feature is found to be extremely powerful, especially if performing computation on the massively parallel graphical processing units. This thesis explores this capability and shows through different experiments the achievement of significant reduction in processing time. en
dc.description.sponsorship The National Training Directorate, Republic of Sudan en
dc.language.iso en en
dc.publisher De Montfort University en
dc.subject type-2 fuzzy en
dc.subject interval valued fuzzy en
dc.subject measures of uncertainty en
dc.subject GPU applications en
dc.subject alpha cuts en
dc.title Type-2 Fuzzy Alpha-cuts en
dc.type Thesis or dissertation en
dc.publisher.department Faculty of Technology en
dc.publisher.department Centre for Computational Intelligence en
dc.type.qualificationlevel Doctoral en
dc.type.qualificationname PhD en

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