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The Global ETD Search service is a free service for researchers
to find electronic theses and dissertations. This service is
provided by the
Networked Digital Library of Theses and Dissertations.
Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
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Showing 1 to 5 of 5 (0.061 seconds)| 1 |
Comparison of different notions of compactness in the fuzzy topological spaceMorapeli, E Z January 1989 (has links)
Various notions of compactness in a fuzzy topological space have been introduced by different authors. The aim of this thesis is to compare them. We find that in a T₂ space (in the sense that no fuzzy net converges to two fuzzy points with different supports) all these notions are equivalent for the whole space. Furthermore, for N-compactness and f-compactness (being the only notions that are defined for an arbitrary fuzzy subset) we have equivalence under a stronger condition, namely, a T₂ space in the sense that every prime prefilter has an adherence that is non-zero in at most one point
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Topological Framework for Digital Image Analysis with Extended Interior and Closure OperatorsFashandi, Homa 25 September 2012 (has links)
The focus of this research is the extension of topological operators with the addition
of a inclusion measure. This extension is carried out in both crisp and fuzzy topological
spaces. The mathematical properties of the new operators are discussed and compared with
traditional operators. Ignoring small errors due to imperfections and noise in digital images
is the main motivation in introducing the proposed operators. To show the effectiveness of
the new operators, we demonstrate their utility in image database classification and shape
classification. Each image (shape) category is modeled with a topological space and the
interior of the query image is obtained with respect to different topologies. This novel way
of looking at the image categories and classifying a query image shows some promising
results. Moreover, the proposed interior and closure operators with inclusion degree is
utilized in mathematical morphology area. The morphological operators with inclusion
degree outperform traditional morphology in noise removal and edge detection in a noisy
environment
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Topological Framework for Digital Image Analysis with Extended Interior and Closure OperatorsFashandi, Homa 25 September 2012 (has links)
The focus of this research is the extension of topological operators with the addition
of a inclusion measure. This extension is carried out in both crisp and fuzzy topological
spaces. The mathematical properties of the new operators are discussed and compared with
traditional operators. Ignoring small errors due to imperfections and noise in digital images
is the main motivation in introducing the proposed operators. To show the effectiveness of
the new operators, we demonstrate their utility in image database classification and shape
classification. Each image (shape) category is modeled with a topological space and the
interior of the query image is obtained with respect to different topologies. This novel way
of looking at the image categories and classifying a query image shows some promising
results. Moreover, the proposed interior and closure operators with inclusion degree is
utilized in mathematical morphology area. The morphological operators with inclusion
degree outperform traditional morphology in noise removal and edge detection in a noisy
environment
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On some results of analysis in metric spaces and fuzzy metric spacesAphane, Maggie 12 1900 (has links)
The notion of a fuzzy metric space due to George and Veeramani has many
advantages in analysis since many notions and results from classical metric space
theory can be extended and generalized to the setting of fuzzy metric spaces, for
instance: the notion of completeness, completion of spaces as well as extension of
maps. The layout of the dissertation is as follows:
Chapter 1 provide the necessary background in the context of metric spaces, while
chapter 2 presents some concepts and results from classical metric spaces in the
setting of fuzzy metric spaces. In chapter 3 we continue with the study of fuzzy
metric spaces, among others we show that: the product of two complete fuzzy metric
spaces is also a complete fuzzy metric space.
Our main contribution is in chapter 4. We introduce the concept of a standard
fuzzy pseudo metric space and present some results on fuzzy metric identification.
Furthermore, we discuss some properties of t-nonexpansive maps. / Mathematical Sciences / M. Sc. (Mathematics)
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On some results of analysis in metric spaces and fuzzy metric spacesAphane, Maggie 12 1900 (has links)
The notion of a fuzzy metric space due to George and Veeramani has many
advantages in analysis since many notions and results from classical metric space
theory can be extended and generalized to the setting of fuzzy metric spaces, for
instance: the notion of completeness, completion of spaces as well as extension of
maps. The layout of the dissertation is as follows:
Chapter 1 provide the necessary background in the context of metric spaces, while
chapter 2 presents some concepts and results from classical metric spaces in the
setting of fuzzy metric spaces. In chapter 3 we continue with the study of fuzzy
metric spaces, among others we show that: the product of two complete fuzzy metric
spaces is also a complete fuzzy metric space.
Our main contribution is in chapter 4. We introduce the concept of a standard
fuzzy pseudo metric space and present some results on fuzzy metric identification.
Furthermore, we discuss some properties of t-nonexpansive maps. / Mathematical Sciences / M. Sc. (Mathematics)
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