Abstract
In terms of rough set theory, information-theoretical measures have been introduced to implement uncertainty measurements and system applications, and their robust construction and in-depth development based on hierarchy and granularity become required and valuable. According to the existing complement-entropy system, a weighted complement-entropy system is established by tri-level granular structures of decision table, and its basic properties and systematic equivalency are revealed. Firstly, Bayes' probability formula at micro-bottom induces a mathematical transformation and hierarchical evolution, and three-way weighted complement-entropies are constructed at both meso-middle and macro-top to achieve the hierarchy, systematicness, monotonicity, and algorithm. Secondly, the classical complement-entropy system is hierarchically decomposed to meso-middle and micro-bottom, and the equivalency between both complement-entropy systems is achieved. Finally, relevant measures and properties are effectively verified by table examples and data experiments. This study hierarchically establishes three-way weighted complement-entropies to develop and interpret the traditional complement-entropies, thus facilitating information optimization and uncertainty applications.
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Lingyu Tang
Lingyu Tang received the BSc degree in mathematics from Huaihua college, Huaihua, China, in 2007 and the MSc degree in mathematics from Sichuan Normal University, Chengdu, China, in 2018. She is currently a doctoral student in School of Mathematical Sciences, Sichuan Normal University. Her research interests include rough set theory and information system.
Xianyong Zhang
Xianyong Zhang received the BSc, MSc, and PhD degrees in mathematics from Sichuan Normal University, Chengdu, China, in 2001, 2004, and 2011, respectively. He completed a two-year visiting research in University of Regina, Saskatchewan, Canada and a two-year postoral work in Tongji University, Shanghai, China. He is currently a professor and a doctoral tutor in School of Mathematical Sciences, Sichuan Normal University. His research interests include rough set theory, information system, granular computing, and data mining.
Zhiwen Mo
Zhiwen Mo received the BSc and MSc degrees in mathematics from Sichuan Normal University, Chengdu, China, in 1985 and 1988, respectively, and the PhD degree in computer and communication from Southwest Jiaotong University, Chengdu, China, in 2005. He is currently a professor and a doctoral tutor in School of Mathematical Sciences, Sichuan Normal University. His research interests include fuzzy set theory, rough set theory, uncertainty analysis, and quantum computing.