覆蓋粗集的覆蓋約簡及拓?fù)涫窖芯?/H1>
發(fā)布時(shí)間：2018-01-05 21:08
本文關(guān)鍵詞：覆蓋粗集的覆蓋約簡及拓?fù)涫窖芯?/strong> 出處：《揚(yáng)州大學(xué)》2017年碩士論文 論文類型：學(xué)位論文
更多相關(guān)文章： 覆蓋粗集 廣義近似空間 拓?fù)?/b> 粗糙連續(xù) 分離性 緊性 覆蓋(飽和)約簡 誘導(dǎo)拓?fù)?/b> 誘導(dǎo)粗集
【摘要】：波蘭數(shù)學(xué)家Pawlak于1982年提出了處理不確定性問題的粗糙集理論,它作為一種數(shù)據(jù)分析處理理論,已成為信息科學(xué)最為活躍的研究領(lǐng)域之一,并被成功地應(yīng)用于醫(yī)藥科學(xué)、材料科學(xué)、管理科學(xué)等領(lǐng)域.廣義近似空間(又稱關(guān)系粗集)及覆蓋近似空間(又稱覆蓋粗集)是對(duì)Pawlak經(jīng)典粗集模型的重要推廣.對(duì)覆蓋粗集類似拓?fù)淇臻g中的性質(zhì)及其約簡的探究是研究覆蓋粗集的重要內(nèi)容.本文利用覆蓋粗集的覆蓋作為子基誘導(dǎo)了一個(gè)拓?fù)淇臻g,定義了覆蓋粗集的多種分離性、緊性等概念,并研究了它們的性質(zhì)及相互關(guān)系.此外對(duì)關(guān)系粗集利用其誘導(dǎo)覆蓋粗集定義了 s-緊,p-緊和雙緊等緊性,并研究了它們的關(guān)系及在粗糙連續(xù)映射下的保持性.本文還研究了覆蓋粗集的覆蓋約簡與覆蓋飽和約簡,證明了當(dāng)U有限時(shí)覆蓋約簡是存在的,而覆蓋飽和約簡不僅存在而且唯一并給出了可行的算法求解覆蓋飽和約簡.本文共分為五章.第一章是引言與預(yù)備,簡單介紹粗糙集理論的發(fā)展概況及本文寫作背景,同時(shí)給出了若干預(yù)備知識(shí).第二章引入誘導(dǎo)關(guān)系粗集和誘導(dǎo)覆蓋粗集,給出了幾種覆蓋粗集誘導(dǎo)關(guān)系粗集及關(guān)系粗集誘導(dǎo)覆蓋粗集的方式.第三章借助覆蓋粗集所誘導(dǎo)的拓?fù)淇臻g的拓?fù)涠x了覆蓋粗集的分離性并給出了它們的刻畫.借助誘導(dǎo)覆蓋粗集的緊性,定義了廣義近似空間的s-緊,p-緊和雙緊,并研究了這三種緊性與關(guān)系緊、拓?fù)渚o之間的關(guān)系.同時(shí)討論了上述五種緊性在粗糙連續(xù)映射下的保持性.第四章對(duì)于覆蓋粗集引入了覆蓋約簡,覆蓋飽和約簡的概念和覆蓋的核的概念,研究了覆蓋約簡和覆蓋飽和約簡的相關(guān)性質(zhì).證明了當(dāng)論域有限時(shí)覆蓋約簡的存在性及覆蓋飽和約簡的存在唯一性.說明了覆蓋約簡不必是覆蓋飽和約簡,覆蓋飽和約簡也不必是覆蓋約簡,并給出覆蓋約簡成為覆蓋飽和約簡的特定條件.第五章總結(jié)了本文的主要工作以及接下來需要進(jìn)一步探究的課題.
[Abstract]:Poland mathematician Pawlak proposed to deal with the uncertainty problem of rough set theory in 1982, it is a kind of data analysis theory, has become one of the most active research in the field of information science, and has been successfully applied in medical science, materials science, management science and other fields. Generalized approximate space (called rough set) and the covering approximation space (also called covering rough set) is an important extension to Pawlak classic rough set model. To explore the nature and the reduction of covering rough set is similar in topological spaces is an important research content of covering rough set. This paper use the covering rough set covering as a sub base induces a topological space, the definition of a variety of separation covering rough sets, the concept of compactness, and studied their properties and relations. In addition to the induction of covering rough set s- is defined by the tight relationship between rough sets, p- and double tight tight tight, and research Their relationship and in the rough continuous mapping of retention. This paper also studies the coverage reduction of covering rough set and saturation coverage reduction, it is proved that when U limited coverage reduction exists, and the existence and uniqueness of saturation coverage reduction algorithm and gives the feasible coverage saturation reduction. This article is divided into the five chapter. The first chapter is the introduction and preparation, introduces the development of rough set theory survey and the background of this writing, and gives some preliminary knowledge. The second chapter introduced the induced relations between rough sets and rough sets are given guidance coverage, several covering rough set relationship induced by rough set and rough set relationship by covering rough set approach. The third chapter with topological topological space covering rough set by definition is given and the separation of covering rough set are depicted. The compactness induced covering rough set, the definition of the generalized approximate space s- Tight, tight and p- double tight, and study the three kinds of compactness and tight relationship, relationship between compact topology. At the same time keep in rough continuous mapping. The five kinds of compactness are discussed. The fourth chapter for covering rough set is introduced covering reduction, the concept of coverage reduction and coverage of the saturated nucleus the concept, properties and saturation coverage coverage reduction reduction. We prove the existence and uniqueness of saturation coverage reduction when the domain of finite covering reduction. The coverage reduction does not need to be covered with saturation coverage reduction, reduction need not be saturated covering reduction, and the reduction of a certain condition coverage saturation reduction. The fifth chapter summarizes the main work of this paper, then the need to further explore the topic.
【學(xué)位授予單位】：揚(yáng)州大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TP18
，
本文編號(hào)：1384828
本文鏈接：http://sikaile.net/kejilunwen/zidonghuakongzhilunwen/1384828.html
本文關(guān)鍵詞：覆蓋粗集的覆蓋約簡及拓?fù)涫窖芯?/strong> 出處：《揚(yáng)州大學(xué)》2017年碩士論文 論文類型：學(xué)位論文
更多相關(guān)文章： 覆蓋粗集 廣義近似空間 拓?fù)?/b> 粗糙連續(xù) 分離性 緊性 覆蓋(飽和)約簡 誘導(dǎo)拓?fù)?/b> 誘導(dǎo)粗集
【摘要】：波蘭數(shù)學(xué)家Pawlak于1982年提出了處理不確定性問題的粗糙集理論,它作為一種數(shù)據(jù)分析處理理論,已成為信息科學(xué)最為活躍的研究領(lǐng)域之一,并被成功地應(yīng)用于醫(yī)藥科學(xué)、材料科學(xué)、管理科學(xué)等領(lǐng)域.廣義近似空間(又稱關(guān)系粗集)及覆蓋近似空間(又稱覆蓋粗集)是對(duì)Pawlak經(jīng)典粗集模型的重要推廣.對(duì)覆蓋粗集類似拓?fù)淇臻g中的性質(zhì)及其約簡的探究是研究覆蓋粗集的重要內(nèi)容.本文利用覆蓋粗集的覆蓋作為子基誘導(dǎo)了一個(gè)拓?fù)淇臻g,定義了覆蓋粗集的多種分離性、緊性等概念,并研究了它們的性質(zhì)及相互關(guān)系.此外對(duì)關(guān)系粗集利用其誘導(dǎo)覆蓋粗集定義了 s-緊,p-緊和雙緊等緊性,并研究了它們的關(guān)系及在粗糙連續(xù)映射下的保持性.本文還研究了覆蓋粗集的覆蓋約簡與覆蓋飽和約簡,證明了當(dāng)U有限時(shí)覆蓋約簡是存在的,而覆蓋飽和約簡不僅存在而且唯一并給出了可行的算法求解覆蓋飽和約簡.本文共分為五章.第一章是引言與預(yù)備,簡單介紹粗糙集理論的發(fā)展概況及本文寫作背景,同時(shí)給出了若干預(yù)備知識(shí).第二章引入誘導(dǎo)關(guān)系粗集和誘導(dǎo)覆蓋粗集,給出了幾種覆蓋粗集誘導(dǎo)關(guān)系粗集及關(guān)系粗集誘導(dǎo)覆蓋粗集的方式.第三章借助覆蓋粗集所誘導(dǎo)的拓?fù)淇臻g的拓?fù)涠x了覆蓋粗集的分離性并給出了它們的刻畫.借助誘導(dǎo)覆蓋粗集的緊性,定義了廣義近似空間的s-緊,p-緊和雙緊,并研究了這三種緊性與關(guān)系緊、拓?fù)渚o之間的關(guān)系.同時(shí)討論了上述五種緊性在粗糙連續(xù)映射下的保持性.第四章對(duì)于覆蓋粗集引入了覆蓋約簡,覆蓋飽和約簡的概念和覆蓋的核的概念,研究了覆蓋約簡和覆蓋飽和約簡的相關(guān)性質(zhì).證明了當(dāng)論域有限時(shí)覆蓋約簡的存在性及覆蓋飽和約簡的存在唯一性.說明了覆蓋約簡不必是覆蓋飽和約簡,覆蓋飽和約簡也不必是覆蓋約簡,并給出覆蓋約簡成為覆蓋飽和約簡的特定條件.第五章總結(jié)了本文的主要工作以及接下來需要進(jìn)一步探究的課題.
[Abstract]:Poland mathematician Pawlak proposed to deal with the uncertainty problem of rough set theory in 1982, it is a kind of data analysis theory, has become one of the most active research in the field of information science, and has been successfully applied in medical science, materials science, management science and other fields. Generalized approximate space (called rough set) and the covering approximation space (also called covering rough set) is an important extension to Pawlak classic rough set model. To explore the nature and the reduction of covering rough set is similar in topological spaces is an important research content of covering rough set. This paper use the covering rough set covering as a sub base induces a topological space, the definition of a variety of separation covering rough sets, the concept of compactness, and studied their properties and relations. In addition to the induction of covering rough set s- is defined by the tight relationship between rough sets, p- and double tight tight tight, and research Their relationship and in the rough continuous mapping of retention. This paper also studies the coverage reduction of covering rough set and saturation coverage reduction, it is proved that when U limited coverage reduction exists, and the existence and uniqueness of saturation coverage reduction algorithm and gives the feasible coverage saturation reduction. This article is divided into the five chapter. The first chapter is the introduction and preparation, introduces the development of rough set theory survey and the background of this writing, and gives some preliminary knowledge. The second chapter introduced the induced relations between rough sets and rough sets are given guidance coverage, several covering rough set relationship induced by rough set and rough set relationship by covering rough set approach. The third chapter with topological topological space covering rough set by definition is given and the separation of covering rough set are depicted. The compactness induced covering rough set, the definition of the generalized approximate space s- Tight, tight and p- double tight, and study the three kinds of compactness and tight relationship, relationship between compact topology. At the same time keep in rough continuous mapping. The five kinds of compactness are discussed. The fourth chapter for covering rough set is introduced covering reduction, the concept of coverage reduction and coverage of the saturated nucleus the concept, properties and saturation coverage coverage reduction reduction. We prove the existence and uniqueness of saturation coverage reduction when the domain of finite covering reduction. The coverage reduction does not need to be covered with saturation coverage reduction, reduction need not be saturated covering reduction, and the reduction of a certain condition coverage saturation reduction. The fifth chapter summarizes the main work of this paper, then the need to further explore the topic.
【學(xué)位授予單位】：揚(yáng)州大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TP18
，
本文編號(hào)：1384828
本文鏈接：http://sikaile.net/kejilunwen/zidonghuakongzhilunwen/1384828.html
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