<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Rough set theory is an important theory for the uncertain information processing. The information theoretic measures have been introduced into rough set theory and provided a new effective method in uncertainty measurement and attribute reduction. However, most of them did not consider the hierarchical structure of a decision table (D-Table). Thus, this paper concretely constructs three-way weighted combination-entropies based on the D-Table’s three-layer granular structures and Bayes’ theorem from a new perspective, and reveals the granulation monotonicity and systematic relationships of three-way weighted combination-entropies. The relevant conclusion provides a more complete and updated interpretation of granular computing for the uncertainty measurement, and it also establishes a more effective basis for the quantitative application in attribute reduction.</p></abstract>

Rough set theory is an important theory for the uncertain information processing. The information theoretic measures have been introduced into rough set theory and provided a new effective method in uncertainty measurement and attribute reduction. However, most of them did not consider the hierarchical structure of a decision table (D-Table). Thus, this paper concretely constructs three-way weighted combination-entropies based on the D-Table’s three-layer granular structures and Bayes’ theorem from a new perspective, and reveals the granulation monotonicity and systematic relationships of three-way weighted combination-entropies. The relevant conclusion provides a more complete and updated interpretation of granular computing for the uncertainty measurement, and it also establishes a more effective basis for the quantitative application in attribute reduction.

Three-way weighted combination-entropies based on three-layer granular structures

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Rough set theory is an important theory for the uncertain information processing. The information theoretic measures have been introduced into rough set theory...

Three-way weighted combination-entropies based on three-layer granular structures

Published Online: Jul 28, 2017

Page range: 329 - 340

Received: Jan 07, 2017

Accepted: Jul 28, 2017

DOI: https://doi.org/10.21042/AMNS.2017.2.00027

Keywords
Rough set, Granular computing, Three-layer granular structures, Three-way weighted combination-entropies, Three-way decisions, Bayes’ theorem

© 2017 Wang Jun, Tang Lingyu, Zhang Xianyong, Luo Yuyan, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Three-way weighted combination-entropies based on three-layer granular structures

Published Online: Jul 28, 2017

Page range: 329 - 340

Received: Jan 07, 2017

Accepted: Jul 28, 2017

DOI: https://doi.org/10.21042/AMNS.2017.2.00027

KeywordsRough set, Granular computing, Three-layer granular structures, Three-way weighted combination-entropies, Three-way decisions, Bayes’ theorem

© 2017 Wang Jun, Tang Lingyu, Zhang Xianyong, Luo Yuyan, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Rough set, Granular computing, Three-layer granular structures, Three-way weighted combination-entropies, Three-way decisions, Bayes’ theorem