<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...

Structure	Composition	Granular scale	Granular level	Simple name
(1)	U/IND (A), U/IND (D)	Macro	Top	Macro-Top
(2)	U/IND (A), X_j	Meso	Middle	Meso-Middle
(3)	${[x]}_{A}^{i}, X_{j}$ $[x]_A^{i},X_j$	Micro	Bottom	Micro-Bottom

Item	C-Classification	C-Class	D-Classification	D-Class
Mathematical symbol	U/IND (A)	${[x]}_{A}^{i}, i = 1, 2, \dots, n$ $[x]_A^i, i=1,2,\dots,n$	U/IND (D)	X_j, j = 1,2, …, m
Granular essence	Conditional granule set	Conditional granule	Decisional granule set	Decisional granule

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

Publié en ligne: 28 juil. 2017

Pages: 329 - 340

Reçu: 07 janv. 2017

Accepté: 28 juil. 2017

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

Mots clés
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.

Fig. 1

Fig 2

Basic descriptions of a D-Table’s three-layer granular structures

Conditional and decisional classifications and classes

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

Publié en ligne: 28 juil. 2017

Pages: 329 - 340

Reçu: 07 janv. 2017

Accepté: 28 juil. 2017

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

Mots clésRough 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.

Fig. 1

Fig 2

Basic descriptions of a D-Table’s three-layer granular structures

Conditional and decisional classifications and classes

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