Applied Mathematics and Nonlinear Sciences
Journal license

Journal

Applied Mathematics and Nonlinear Sciences


Volume
& Issue

Volume 2, Issue 2


Published
on

July 28, 2017


Pages

329-340


DOI

Article

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

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Authors

Wang Jun Affiliation:
Business School, Sichuan Normal University, Sichuan, China
, Tang Lingyu Affiliation:
School of Mathematical Science, Sichuan Normal University, Sichuan, China
, Zhang Xianyong Affiliation:
School of Mathematical Science, Sichuan Normal University, Sichuan, China
and Luo Yuyan Affiliation:
Management Science School, Chengdu University of Technology, Sichuan, China


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.


Keywords

Rough set, Granular computing, Three-layer granular structures, Three-way weighted combination-entropies, Three-way decisions, Bayes’ theorem, 68T30, 68T37


Citation

Jun, W., Lingyu, T., Xianyong, Z., & Yuyan, L. (2017). Three-way weighted combination-entropies based on three-layer granular structures. Applied Mathematics and Nonlinear Sciences, 2(2), 329–340. https://doi.org/10.21042/AMNS.2017.2.00027

Published by: Engineering Journals

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