The objective of this thesis is a survey of crisp and fuzzy sober topological spaces. We begin by examining sobriety of crisp topological spaces. We then extend this to the L- topological case and obtain analogous results and characterizations to those of the crisp case. We then brie y examine semi-sobriety of (L;M)-topological spaces.

Thesis (M. Phil.)--Chinese University of Hong Kong, 1998. / Description based on contents viewed Mar. 13, 2007; title from title screen. Includes bibliographical references (p. 99-103). Also available in print.

Image segmentation is an important step in the image analysis process. Current image segmentation techniques, however, require that the user tune several parameters in order to obtain maximum segmentation accuracy, a computationally inefficient approach, especially when a large number of images must be processed sequentially in real time. Another major challenge, particularly with medical image analysis, is the discrepancy between objective measures for assessing and guiding the segmentation process, on the one hand, and the subjective perception of the end users (e.g., clinicians), on the other. Hence, the setting and adjustment of parameters for medical image segmentation should be performed in a manner that incorporates user feedback. Despite the substantial number of techniques proposed in recent years, accurate segmentation of digital images remains a challenging task for automated computer algorithms. Approaches based on machine learning hold particular promise in this regard because, in many applications, including medical image analysis, frequent user intervention can be assumed as a means of correcting the results, thereby generating valuable feedback for algorithmic learning. This thesis presents an investigation of the use of evolving fuzzy systems for designing a method that overcomes the problems associated with medical image segmentation. An evolving fuzzy system can be trained using a set of invariant features, along with their optimum parameters, which act as a target for the system. Evolving fuzzy systems are also capable of adjusting parameters based on online updates of their rule base. This thesis proposes three different approaches that employ an evolving fuzzy system for the continual adjustment of the parameters of any medical image segmentation technique. The first proposed approach is based on evolving fuzzy image segmentation (EFIS). EFIS can adjust the parameters of existing segmentation methods and switch between them or fuse their results. The evolving rules have been applied for breast ultrasound images, with EFIS being used to adjust the parameters of three segmentation methods: global thresholding, region growing, and statistical region merging. The results for ten independent experiments for each of the three methods show average increases in accuracy of 5\%, 12\% and 9\% respectively. A comparison of the EFIS results with those obtained using five other thresholding methods revealed improvements. On the other hand, EFIS has some weak points, such as some fixed parameters and an inefficient feature calculation process. The second approach proposed as a means of overcoming the problems with EFIS is a new version of EFIS, called self-configuring EFIS (SC-EFIS). SC-EFIS uses the available data to estimate all of the parameters that are fixed in EFIS and has a feature selection process that selects suitable features based on current data. SC-EFIS was evaluated using the same three methods as for EFIS. The results show that SC-EFIS is competitive with EFIS but provides a higher level of automation. In the third approach, SC-EFIS is used to dynamically adjust more than one parameter, for example, three parameters of the normalized cut (N-cut) segmentation technique. This method, called multi-parametric SC-EFIS (MSC-EFIS), was applied to magnetic resonance images (MRIs) of the bladder and to breast ultrasound images. The results show the ability of MSC-EFIS to adjust multiple parameters. For ten independent experiments for each of the bladder and the breast images, this approach produced average accuracies that are 8\% and 16\% higher respectively, compared with their default values. The experimental results indicate that the proposed algorithms show significant promise in enhancing image segmentation, especially for medical applications.

No description available.

In this thesis we first extend the notion of fuzzy normality to the notion of normality of a fuzzy subgroup in another fuzzy group. This leads to the study of normal series of fuzzy subgroups, and this study includes solvable and nilpotent fuzzy groups, and the fuzzy version of the Jordan-Hõlder Theorem. Furthermore we use the notion of normality to study products and direct products of fuzzy subgroups. We present a notion of fuzzy isomorphism which enables us to state and prove the three well-known isomorphism theorems and the fact that the internal direct product of two normal fuzzy subgroups is isomorphic to the external direct product of the same fuzzy subgroups. A brief discussion on fuzzy subgroups generated by fuzzy subsets is also presented, and this leads to the fuzzy version of the Basis Theorem. Finally, the notion of direct product enables us to study decomposable and indecomposable fuzzy subgroups, and this study includes the fuzzy version of the Remak-Krull-Schmidt Theorem.

No description available.

No description available.

No description available.

鄧國章. / Thesis (M.A.)--香港中文大學硏究院地理學部. / Includes bibliographical references (leaves 215-228). / Deng Guozhang. / Thesis (M.A.)--Xianggang Zhong wen da xue yan jiu yuan di li xue bu. / Chapter 第一章 --- 導論 --- p.1 / Chapter 1.1 --- 研究目的 --- p.1 / Chapter 1.2 --- 研究意義 --- p.7 / Chapter 1.2.1 --- 方法學上的意義 --- p.7 / Chapter 1.2.2 --- 地理學上的意義 --- p.8 / Chapter 1.2.3 --- 應用上的意義 --- p.9 / Chapter 1.3 --- 研究範圍 --- p.10 / Chapter 1.4 --- 論文結構概述 --- p.12 / Chapter 第二章 --- 文獻簡讀 --- p.15 / Chapter 2.1 --- 分類與區劃的意義 --- p.15 / Chapter 2.1.1 --- 分類與區劃 --- p.15 / Chapter 2.1.2 --- 區域的類型 --- p.18 / Chapter 2.1.3 --- 區劃的方法　 --- p.23 / Chapter 2.2 --- 氣候分類 --- p.27 / Chapter 2.2.1 --- 氣候分類的目的及意義　　 --- p.27 / Chapter 2.2.2 --- 氣候分類的類型及方法 --- p.29 / Chapter 2.2.3 --- 柯本氏氣候分類法 --- p.31 / Chapter 2.3 --- 中國氣候區劃 --- p.41 / Chapter 2.3.1 --- 中國氣候區劃歷史概況 --- p.41 / Chapter 2.3.2 --- 應用柯本氏氣候分類法於中國氣候區劃的經驗 --- p.44 / Chapter 2.4 --- 糢糊集合論於分類及區畫間題上的應用 --- p.47 / Chapter 2.4.1 --- 糢糊集合論於分類及區劃上的應用 --- p.47 / Chapter 2.4.2 --- 糢糊集合論於氣候區劃的應用 --- p.50 / Chapter 第三章 --- 研究方法 --- p.53 / Chapter 3.1 --- 應用模糊集合論於氣候分類之理論基璴 　 --- p.53 / Chapter 3.1.1 --- 集合與區域 --- p.53 / Chapter 3.1.2 --- 模糊集合的基本概念及運算 --- p.54 / Chapter 3.2 --- 氣候區的釐訂及區域界綫的劃定方法 --- p.68 / Chapter 3.2.1 --- 氣候區的描述 --- p.68 / Chapter 3.2.2 --- 氣候區的重疊與分割 --- p.75 / Chapter 3.3 --- 數據資料處理方法 --- p.80 / Chapter 3.3.1 --- 數據搜集方法 --- p.80 / Chapter 3.3.2 --- 站點分佈情況 --- p.80 / Chapter 3.3.3 --- 資料整理方法 --- p.82 / Chapter 3.4 --- 注釋 --- p.85 / Chapter 第四章 --- 柯本氏氣候分類系統的普通集合表示 --- p.86 / Chapter 4.1 --- 柯本氏氣候類型可視一組集合 --- p.86 / Chapter 4.2 --- 結果及分析 --- p.96 / Chapter 第五章 --- 柯本氏氣侯分類之模楜集合分析－隸屬度分析 --- p.99 / Chapter 5.1 --- 訂定隸屬涵數方法及區劃步驟 --- p.99 / Chapter 5.2 --- 結果及隸屬度分析 　　 --- p.108 / Chapter 5.3 --- 中國氣候區的劃定 --- p.125 / Chapter 5.4 --- 小結 --- p.140 / Chapter 第六章 --- 柯本氏氣類之模糊集合分析－分割度分析 --- p.143 / Chapter 6.1 --- 分割與區界 --- p.143 / Chapter 6.2 --- 結果及分析 --- p.146 / Chapter 6.3 --- 中國氣候區重疊地帶的劃訂 --- p.155 / Chapter 6.4 --- 小結 --- p.166 / Chapter 6.5 --- 注釋 --- p.169 / Chapter 第七章 --- 柯本氏氣候分類法的改進 --- p.170 / Chapter 7.1 --- 柯本氏氣候分類法的改善 --- p.170 / Chapter 7.2 --- 改良後的柯本氏範式之中國氣候區劃 --- p.186 / Chapter 7.3 --- 與中國植被區的劃配合情況 　 --- p.186 / Chapter 7.4 --- 與中國土壤區劃的配合情況　　 --- p.194 / Chapter 第八章 --- 後語 --- p.208 / Chapter 8.1 --- 研究結果要點重申 --- p.208 / Chapter 8.2 --- 研究限制 --- p.210 / Chapter 8.3 --- 研究展望 --- p.213 / 參考文獻 --- p.215 / 附錄 / Chapter I --- 中國各省、市、自治區志面　 --- p.229 / Chapter II --- 柯氏氣候類型的隸屬函數 --- p.235 / Chapter III --- 電腦計算程式 --- p.254 / Chapter IV --- 隸屬度計算結果 --- p.259 / Chapter （一） --- 原本的柯本氏氣候類型的隸屬度計算結果 --- p.259 / Chapter （二） --- 改良後的柯本氏氣候類型的隸屬度計算結果 --- p.265

by Lam Wai. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1988. / Bibliography: leaves 216-220.