Thesis (Ph. D.)--Ohio University, June, 2001. / Title from PDF t.p.

Rough sets have been studied for over 30 years, and the basic concepts of lower and upper approximations have been analysed in detail, yet nowhere has the idea of an `optimal' rough approximation been proposed or investigated. In this thesis, several concepts are used in proposing a generalized definition: measures, rough sets, similarity, and approximation are each surveyed. Measure Theory allows us to generalize the definition of the `size' for a set. Rough set theory is the foundation that we use to define the term `optimal' and what constitutes an `optimal rough set'. Similarity indexes are used to compare two sets, and determine how alike or different they are. These sets can be rough or exact. We use similarity indexes to compare sets to intermediate approximations, and isolate the optimal rough sets. The historical roots of these concepts are explored, and the foundations are formally defined. A definition of an optimal rough set is proposed, as well as a simple algorithm to find it. Properties of optimal approximations such as minimum, maximum, and symmetry, are explored, and examples are provided to demonstrate algebraic properties and illustrate the mechanics of the algorithm. / Thesis / Doctor of Philosophy (PhD) / Until now, in the context of rough sets, only an upper and lower approximation had been proposed. Here, an concept of an optimal/best approximation is proposed, and a method to obtain it is presented.

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OLIVEIRA, Henrique Viana. Refinamento de consultas em lógicas de descrição utilizando teoria dos Rough sets. 2012. 111 f. Dissertação (Mestrado em ciência da computação)- Universidade Federal do Ceará, Fortaleza-CE, 2012. / Submitted by Elineudson Ribeiro (elineudsonr@gmail.com) on 2016-07-11T16:33:31Z No. of bitstreams: 1 2012_dis_hvoliveira.pdf: 789598 bytes, checksum: d75ef093adc56cc930f52c1e486ead5a (MD5) / Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2016-07-18T13:43:45Z (GMT) No. of bitstreams: 1 2012_dis_hvoliveira.pdf: 789598 bytes, checksum: d75ef093adc56cc930f52c1e486ead5a (MD5) / Made available in DSpace on 2016-07-18T13:43:45Z (GMT). No. of bitstreams: 1 2012_dis_hvoliveira.pdf: 789598 bytes, checksum: d75ef093adc56cc930f52c1e486ead5a (MD5) Previous issue date: 2012 / Query Refinement consists of methods that modify the terms of a consult aiming the change of its result obtained previously. Refinements can be done of several ways and different approaches can be applied to it. This work proposes to apply methods of Query Refinement based on Rough Set theory, using it as an alternative for the refinement problem. The proposed methods will be grounded in the languages of Description Logics, which are commonly used on problems involving knowledge bases or ontologies representation. Two extensions of Description Logics with the Rough Set theory are introduced in this dissertation. We will prove the complexity of satisfiability of these logics, as well as the complexities of the query refinement methods applied to these logics. Finally, we will show quality measures which will aid to choose the results of the refinements obtained. / Refinamento de consulta consiste de técnicas que modificam os termos de uma consulta com o objetivo de alterar os resultados obtidos inicialmente. Para a realização de tal fim, diversas abordagens podem ser aplicadas e diferentes tipos de refinamentos podem ser considerados. Este trabalho propõe aplicar a teoria dos Rough Sets como uma nova alternativa de solução para o problema. Através das noções presentes nessa teoria, iremos desenvolver técnicas que serão aplicadas nas linguagens de Lógicas de Descrição, que são comumente utilizadas em problemas de representação de bases de conhecimento ou ontologias. Além disso, introduziremos duas extensões de Lógicas de Descrição capazes de representar as operações da teoria dos Rough Sets. Provaremos os resultados de complexidade de decisão dessas duas lógicas, assim como os resultados de complexidade das técnicas de refinamentos desenvolvidas. Por fim, mostraremos métricas de qualidade que poderão ser usadas para melhorar o resultado dos refinamentos obtidos.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Refinamento de consulta consiste de tÃcnicas que modificam os termos de uma consulta com o objetivo de alterar os resultados obtidos inicialmente. Para a realizaÃÃo de tal fim, diversas abordagens podem ser aplicadas e diferentes tipos de refinamentos podem ser considerados. Este trabalho propÃe aplicar a teoria dos Rough Sets como uma nova alternativa de soluÃÃo para o problema. AtravÃs das noÃÃes presentes nessa teoria, iremos desenvolver tÃcnicas que serÃo aplicadas nas linguagens de LÃgicas de DescriÃÃo, que sÃo comumente utilizadas em problemas de representaÃÃo de bases de conhecimento ou ontologias. AlÃm disso, introduziremos duas extensÃes de LÃgicas de DescriÃÃo capazes de representar as operaÃÃes da teoria dos Rough Sets. Provaremos os resultados de complexidade de decisÃo dessas duas lÃgicas, assim como os resultados de complexidade das tÃcnicas de refinamentos desenvolvidas. Por fim, mostraremos mÃtricas de qualidade que poderÃo ser usadas para melhorar o resultado dos refinamentos obtidos. / Query Refinement consists of methods that modify the terms of a consult aiming the change of its result obtained previously. Refinements can be done of several ways and different approaches can be applied to it. This work proposes to apply methods of Query Refinement based on Rough Set theory, using it as an alternative for the refinement problem. The proposed methods will be grounded in the languages of Description Logics, which are commonly used on problems involving knowledge bases or ontologies representation. Two extensions of Description Logics with the Rough Set theory are introduced in this dissertation. We will prove the complexity of satisfiability of these logics, as well as the complexities of the query refinement methods applied to these logics. Finally, we will show quality measures which will aid to choose the results of the refinements obtained.

We investigate the use of the concept of indiscernibilityand vagueness in spatial information systems. To representindiscernibility and vagueness we use rough sets, respectivelyfuzzy sets. We introduce a theoretical model to supportapproximate queries in information systems and we show howthose queries can be used to perform uncertain classi.cations.We also explore how to assess quality of uncertainclassi.cations and ways to compare those classi.cations to eachother in order to assess accuracies. We implement the querylanguage in an SQL relational language to demonstrate thefeasibility of approximate queries and we perform an experimenton real data using uncertain classi.cations.

With the popularization of Internet and the wide use of electronic mails, the number of spam mails grows continuously. The matter has made e-mail users feel inconvenient. If e-mail servers can be integrated with data mining and artificial intelligence techniques and learn spam rules and filter out spam mails automatically, they will help every person who is bothered by spam mails to enjoy a clear e-mail environment. In this research, we propose an architecture called union defense to oppose against the spread of spam mails. Under the architecture, we need a rule-based data mining and artificial intelligence algorithm. Rough sets theory will be a good choice. Rough sets theory was proposed by Palwak, a logician living in Poland. It is a rule-based data mining and artificial intelligence algorithm and suitable to find the potential knowledge of inexact and incomplete data out. This research developed a spam filter based on rough sets theory. It can search for the characteristic rules of spam mails and can use these rules to filter out spam mails. This system set up by this research can be appended to most of existing e-mail servers. Besides, the system support Chinese, Japanese and Korean character sets and overcome the problem that most spam filters only can deal with English mails. We can develop a rule exchange approach between e-mail servers in the future works to realize union defense.

<p>We investigate the use of the concept of indiscernibilityand vagueness in spatial information systems. To representindiscernibility and vagueness we use rough sets, respectivelyfuzzy sets. We introduce a theoretical model to supportapproximate queries in information systems and we show howthose queries can be used to perform uncertain classi.cations.We also explore how to assess quality of uncertainclassi.cations and ways to compare those classi.cations to eachother in order to assess accuracies. We implement the querylanguage in an SQL relational language to demonstrate thefeasibility of approximate queries and we perform an experimenton real data using uncertain classi.cations.</p>

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OLIVEIRA, Henrique Viana. Refinamento de Consultas em Lógicas de Descrição Utilizando Teoria dos Rough Sets. 2012. 111 f. : Dissertação (mestrado) - Universidade Federal do Ceará, Centro de Ciências, Departamento de Computação, Fortaleza-CE, 2012. / Submitted by guaracy araujo (guaraa3355@gmail.com) on 2016-07-01T17:23:02Z No. of bitstreams: 1 2012_dis_hvoliveira.pdf: 789598 bytes, checksum: d75ef093adc56cc930f52c1e486ead5a (MD5) / Approved for entry into archive by guaracy araujo (guaraa3355@gmail.com) on 2016-07-01T17:23:47Z (GMT) No. of bitstreams: 1 2012_dis_hvoliveira.pdf: 789598 bytes, checksum: d75ef093adc56cc930f52c1e486ead5a (MD5) / Made available in DSpace on 2016-07-01T17:23:47Z (GMT). No. of bitstreams: 1 2012_dis_hvoliveira.pdf: 789598 bytes, checksum: d75ef093adc56cc930f52c1e486ead5a (MD5) Previous issue date: 2012 / Query Refinement consists of methods that modify the terms of a consult aiming the change of its result obtained previously. Refinements can be done of several ways and different approaches can be applied to it. This work proposes to apply methods of Query Refinement based on Rough Set theory, using it as an alternative for the refinement problem. The proposed methods will be grounded in the languages of Description Logics, which are commonly used on problems involving knowledge bases or ontologies representation. Two extensions of Description Logics with the Rough Set theory are introduced in this dissertation. We will prove the complexity of satisfiability of these logics, as well as the complexities of the query refinement methods applied to these logics. Finally, we will show quality measures which will aid to choose the results of the refinements obtained. / Refinamento de consulta consiste de técnicas que modificam os termos de uma consulta com o objetivo de alterar os resultados obtidos inicialmente. Para a realização de tal fim, diversas abordagens podem ser aplicadas e diferentes tipos de refinamentos podem ser considerados. Este trabalho propõe aplicar a teoria dos Rough Sets como uma nova alternativa de solução para o problema. Através das noções presentes nessa teoria, iremos desenvolver técnicas que serão aplicadas nas linguagens de Lógicas de Descrição, que são comumente utilizadas em problemas de representação de bases de conhecimento ou ontologias. Além disso, introduziremos duas extensões de Lógicas de Descrição capazes de representar as operações da teoria dos Rough Sets. Provaremos os resultados de complexidade de decisão dessas duas lógicas, assim como os resultados de complexidade das técnicas de refinamentos desenvolvidas. Por fim, mostraremos métricas de qualidade que poderão ser usadas para melhorar o resultado dos refinamentos obtidos.