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Applied Mathematics and Nonlinear Sciences

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Available online: July 28, 2017

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

Wang Jun, Tang Lingyu, Zhang Xianyong, Luo Yuyan
Volume 2 - Issue 2.     Year 2017.     Pages 329–340.

DOI: 10.21042/AMNS.2017.2.00027


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.

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Applied Mathematics, Nonlinear Sciences


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