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Reasoning with Rough Sets and Paraconsistent Rough Sets
Linköping University, The Institute of Technology. Linköping University, Department of Science and Technology, Media and Information Technology.
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis presents an approach to knowledge representation combining rough sets and para-consistent logic programming.

The rough sets framework proposes a method to handle a specific type of uncertainty originating from the fact that an agent may perceive different objects of the universe as being similar, although they may have di®erent properties. A rough set is then defined by approximations taking into account the similarity between objects. The number of applications and the clear mathematical foundation of rough sets techniques demonstrate their importance.

Most of the research in the rough sets field overlooks three important aspects. Firstly, there are no established techniques for defining rough concepts (sets) in terms of other rough concepts and for reasoning about them. Secondly, there are no systematic methods for integration of domain and expert knowledge into the definition of rough concepts. Thirdly, some additional forms of uncertainty are not considered: it is assumed that knowledge about similarities between objects is precise, while in reality it may be incomplete and contradictory; and, for some objects there may be no evidence about whether they belong to a certain concept.

The thesis addresses these problems using the ideas of paraconsistent logic programming, a recognized technique which makes it possible to represent inconsistent knowledge and to reason about it. This work consists of two parts, each of which proposes a di®erent language. Both languages cater for the definition of rough sets by combining lower and upper approximations and boundaries of other rough sets. Both frameworks take into account that membership of an object into a concept may be unknown.

The fundamental difference between the languages is in the treatment of similarity relations. The first language assumes that similarities between objects are represented by equivalence relations induced from objects with similar descriptions in terms of a given number of attributes. The second language allows the user to define similarity relations suitable for the application in mind and takes into account that similarity between objects may be imprecise. Thus, four-valued similarity relations are used to model indiscernibility between objects, which give rise to rough sets with four-valued approximations, called paraconsistent rough sets. The semantics of both languages borrows ideas and techniques used in paraconsistent logic programming. Therefore, a distinctive feature of our work is that it brings together two major fields, rough sets and paraconsistent logic programming.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press , 2010. , 43 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1307
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-60794ISBN: 978-91-7393-411-4 (print)OAI: oai:DiVA.org:liu-60794DiVA: diva2:359138
Public defence
2010-11-19, K3, Kåkenhus, Campus Norrköping, Linköpings universitet, Norrköping, 09:15
Opponent
Supervisors
Available from: 2010-10-26 Created: 2010-10-26 Last updated: 2016-06-10Bibliographically approved
List of papers
1. A framework for reasoning with rough sets
Open this publication in new window or tab >>A framework for reasoning with rough sets
2005 (English)In: Transactions on Rough Sets IV / [ed] James F. Peters and Andrzej Skowron, Springer Berlin/Heidelberg, 2005, Vol. 3700, 178-276 p.Chapter in book (Refereed)
Abstract [en]

Rough sets framework has two appealing aspects. First, it is a mathematical approach to deal with vague concepts. Second, rough set techniques can be used in data analysis to find patterns hidden in the data. The number of applications of rough sets to practical problems in different fields demonstrates the increasing interest in this framework and its applicability. This thesis(1) proposes a language that caters for implicit definitions of rough sets obtained by combining different regions of other rough sets. In this way, concept approximations can be derived by taking into account domain knowledge. A declarative semantics for the language is also discussed. It is then shown that programs in the proposed language can be compiled to extended logic programs under the paraconsistent stable model semantics. The equivalence between the declarative semantics of the language and the declarative semantics of the compiled programs is proved. This transformation provides the computational basis for implementing our ideas. A query language for retrieving information about the concepts represented through the defined rough sets is also discussed. Several motivating applications are described. Finally, an extension of the proposed language with numerical measures is presented. This extension is motivated by the fact that numerical measures are an important aspect in data mining applications.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2005
Series
Lecture Notes in Computer Science, ISSN 0302-9743 (print), 1611-3349 (online) ; 3700
Series
Lecture Notes in Computer Science, ISSN 0302-9743 ; 3700
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-48115 (URN)10.1007/11574798_10 (DOI)978-3-540-29830-4 (ISBN)e-978-3-540-32016-6 (ISBN)3-540-29830-4 (ISBN)
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2013-10-15Bibliographically approved
2. Modelling and Reasoning with Paraconsistent Rough Sets
Open this publication in new window or tab >>Modelling and Reasoning with Paraconsistent Rough Sets
2009 (English)In: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 97, no 4, 405-438 p.Article in journal (Refereed) Published
Abstract [en]

We present a language for defining paraconsistent rough sets and reasoning about them. Our framework relates and brings together two major fields: rough sets [23] and paraconsistent logic programming [9]. To model inconsistent and incomplete information we use a four-valued logic. The language discussed in this paper is based on ideas of our previous work [21, 32, 22] developing a four-valued framework for rough sets. In this approach membership function, set containment and set operations are four-valued, where logical values are t (true), f (false), i (inconsistent) and u (unknown). We investigate properties of paraconsistent rough sets as well as develop a paraconsistent rule language, providing basic computational machinery for our approach.

Keyword
approximate reasoning, rough sets, paraconsistent reasoning, four-valued logics
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-53059 (URN)10.3233/FI-2009-209 (DOI)
Available from: 2010-01-15 Created: 2010-01-15 Last updated: 2017-12-12

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