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Bit-Vector Representation of Dominance-Based Approximation Space

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Transactions on Rough Sets XIII

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 6499))

Abstract

Dominance-based Rough Set Approach (DRSA) introduced by Greco et al. is an extension of Pawlak’s classical rough set theory by using dominance relations in place of equivalence relations for approximating sets of preference ordered decision classes. The elementary granules in DRSA are P-dominating and P-dominated sets. Recently, Chan and Tzeng introduced the concept of indexed blocks for representing dominance-based approximation space with generalized dominance relations on evaluations of objects. This paper shows how to derive indexed blocks from P-dominating and P-dominated sets in DRSA. Approximations are generalized to any family of decision classes in terms of indexed blocks formulated as binary neighborhood systems. We present algorithms for generating indexed blocks from multi-criteria decision tables and for encoding indexed blocks as bit-vectors to facilitate the computation of approximations and rule generation. A new form of representing decision rules by using interval and set-difference operators is introduced, and we give a procedure of how to generate this type of rules that can be implemented as SQL queries.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Akron, Akron, OH, 44325-4003, USA

    Chien-Chung Chan

  2. Department of Business and Entrepreneurial Administration, Kainan University, No. 1 Kainan Road, Luchu, Taoyuan County, 338, Taiwan

    Gwo-Hshiung Tzeng

  3. Institute of Management of Technology, National Chiao Tung University, 1001 Ta-Hsueh Road, Hsinchu, 300, Taiwan

    Gwo-Hshiung Tzeng

Authors
  1. Chien-Chung Chan
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  2. Gwo-Hshiung Tzeng
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Editor information

Editors and Affiliations

  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

  3. Department of Computer Science, The University of Akron, 44325-4003, Akron, OH, USA

    Chien-Chung Chan

  4. Department of Electrical Engineering and Computer Science, The University of Kansas, 66045, Lawrence, KS, USA

    Jerzy W. Grzymala-Busse

  5. Department of Computer Science, University of Regina, SK S4S 0A2, Regina, Canada

    Wojciech P. Ziarko

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Chan, CC., Tzeng, GH. (2011). Bit-Vector Representation of Dominance-Based Approximation Space. In: Peters, J.F., Skowron, A., Chan, CC., Grzymala-Busse, J.W., Ziarko, W.P. (eds) Transactions on Rough Sets XIII. Lecture Notes in Computer Science, vol 6499. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18302-7_1

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  • DOI: https://doi.org/10.1007/978-3-642-18302-7_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-18301-0

  • Online ISBN: 978-3-642-18302-7

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