A framework for reasoning with rough sets
2005 (English)Licentiate thesis, monograph (Other academic)
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.
Most of the current rough sets techniques and software systems based on them only consider rough sets defined explicitly by concrete examples given in tabular form. The previous research mostly disregards the following two problems. The first problem is related with how to define rough sets in terms of other rough sets. The second problem is related with how to incorporate domain or expert knowledge.
This thesis 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 defined. Several motivating applications are described. Finally, an extension of the proposed language with numerical measures is discussed. This extension is motivated by the fact that numerical measures are an important aspect in data mining applications.
Place, publisher, year, edition, pages
Linköping: Linköpings universitet , 2005. , 146 p.
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1144
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-28406Local ID: 13542ISBN: 91-85297-15-1OAI: oai:DiVA.org:liu-28406DiVA: diva2:249212