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A Framework for Reasoning with Rough Sets

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Transactions on Rough Sets IV

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 3700))

Abstract

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 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.

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Authors and Affiliations

  1. Dept. of Science and Technology, Linköping University, S 601 74, Norrköping, Sweden

    Aida Vitória

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  1. Aida Vitória
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  1. Department of Electrical and Computer Engineering, University of Manitoba, R3T 5V6, Winnipeg, Manitoba, Canada

    James F. Peters

  2. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

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Vitória, A. (2005). A Framework for Reasoning with Rough Sets. In: Peters, J.F., Skowron, A. (eds) Transactions on Rough Sets IV. Lecture Notes in Computer Science, vol 3700. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11574798_10

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  • DOI: https://doi.org/10.1007/11574798_10

  • Publisher Name: Springer, Berlin, Heidelberg

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