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Incremental method of updating approximations in DRSA under variations of multiple objects

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Abstract

Dominance-based rough sets approach (DRSA) uses dominance relations to substitute equivalence relations in conventional rough set models so that it can handle preference-ordered information. Up to date, DRSA has been widely used in multi-criteria decision-making problems. In these real-life problems, however, since the collected data are evolving from time to time, there are often some variations of the attribute sets or object sets. In the dynamic information systems, the frequent update of the lower and upper approximations of DRSA is an necessary step for further updating attribute reducts and decision rules which are important for knowledge discovery and decision-making. Incrementally updating approximations is a type of effective methods to reduce the computational load when any variation occurs. Most of current studies on incremental methods only consider conventional rough set models and the situation when a single object varies in an information system. In this paper, we focus on the variations of object sets and discuss incremental methods of updating approximations of DRSA when multiple objects changed. The updating principles in different dynamic situations are given with detail proofs and the corresponding incremental algorithms are also developed. The experimental evaluations on 12 UCI data sets show that our proposed incremental approaches effectively reduce the computational time in comparison with the non-incremental approach as well as a typical incremental method in the literature.

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Abbreviations

U :

Universe

\(U^{{\prime }}\) :

The updated universe

X :

A target concept (decision class)

\(X^{{\prime }}\) :

The updated decision class

\([x]_{C}^{ \le } /[x]_{C}^{ \ge }\) :

Dominating/dominated set of object x

\([x]_{C}^{{{\prime } \le }} /[x]_{C}^{{{\prime } \ge }}\) :

The updated dominating/dominated set of x

\(X^{ - }\) :

The set of removed objects

\(X^{ + }\) :

The set of inserted objects

\(\underline{R}_{C}^{ \le } \left( X \right)\) :

Lower approximation of X

\(\underline{R}_{C}^{ \le } (X^{{\prime }} )\) :

The updated lower approximation of X

\(\overline{R}_{C}^{ \le } \left( X \right)\) :

Upper approximation of X

\(\overline{R}_{C}^{ \le } (X^{{\prime }} )\) :

The updated upper approximation of X

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Acknowledgment

This work is supported by the National Natural Science Foundations of China (Nos. 61170040,61473111), the Natural Science Foundations of Hebei Province (Nos. F2014201100, A2014201003), and Postgraduate Innovation Foundations of Hebei University (No. X2015059).

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Authors and Affiliations

  1. Key Laboratory of Machine Learning and Computational Intelligence, College of Mathematics and Information Science, Hebei University, Baoding, 071002, China

    Yan Li & Yongfei Jin

  2. Laboratory for Statistical Genomics and Systems Biology, Department of Environmental Health, University of Cincinnati College of Medicine, Cincinnati, OH, USA

    Xiaodian Sun

Authors
  1. Yan Li
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  2. Yongfei Jin
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  3. Xiaodian Sun
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Correspondence to Yan Li.

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Li, Y., Jin, Y. & Sun, X. Incremental method of updating approximations in DRSA under variations of multiple objects. Int. J. Mach. Learn. & Cyber. 9, 295–308 (2018). https://doi.org/10.1007/s13042-015-0477-8

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  • DOI: https://doi.org/10.1007/s13042-015-0477-8

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