A weighted complement-entropy system based on tri-level granular structures

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.

Keywords:

• Rough set theory
• information theory
• complement entropy
• uncertainty
• granular computing
• tri-level granular structures
• three-way decisions

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors thank both the editors and reviewers for their valuable suggestions, which substantially improve this paper. This work was supported by National Natural Science Foundation of China (61673285 and 11671284), Sichuan Science and Technology Project of China (20YFG0290 and 19YYJC2845), and a joint research project of Laurent Mathematics Center of Sichuan Normal University and National-Local Joint Engineering Laboratory of System Credibility Automatic Verification.

Notes on contributors

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.