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

Wang Jun

Wang Jun

Business School, Sichuan Normal UniversitySichuan, China
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Jun, Wang
, 
Tang Lingyu

Tang Lingyu

School of Mathematical Science, Sichuan Normal UniversitySichuan, China
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Lingyu, Tang
, 
Zhang Xianyong

Zhang Xianyong

School of Mathematical Science, Sichuan Normal UniversitySichuan, China
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Xianyong, Zhang
 and 
Luo Yuyan

Luo Yuyan

Management Science School, Chengdu University of TechnologySichuan, China
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Yuyan, Luo
  
Jul 28, 2017
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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
© 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

Hierarchical/Granular relationships of the D-Table’s three-layer granular structures.
Hierarchical/Granular relationships of the D-Table’s three-layer granular structures.

Fig 2

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

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

StructureCompositionGranular scaleGranular levelSimple name
(1)U/IND (A), U/IND (D)MacroTopMacro-Top
(2)U/IND (A), XjMesoMiddleMeso-Middle
(3)[x]Ai,Xj $[x]_A^{i},X_j$ MicroBottomMicro-Bottom

Conditional and decisional classifications and classes

ItemC-ClassificationC-ClassD-ClassificationD-Class
Mathematical symbolU/IND (A)[x]Ai,i=1,2,…,n $[x]_A^i, i=1,2,\dots,n$ U/IND (D)Xj, j = 1,2, …, m
Granular essenceConditional granule setConditional granuleDecisional granule setDecisional granule
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