Measures of uncertainty for a fuzzy probabilistic information system

Abstract

Fuzzy probabilistic information system (FPIS), a combination of some fuzzy relations on the same universe which satisfies probability distribution, can be regarded as an information system (IS) with fuzzy relations under the probability environment. This means that three types of uncertainty: roughness fuzziness and probability are integrated into an IS. This paper aims to measure the uncertainty of a FPIS. Firstly, information granulation in a FPIS is proposed. Then, information entropy and rough entropy in a FPIS are proposed. Moreover, information amount in a FPIS is also investigated. Finally, the feasibility of the proposed measures are verified by a numerical example, and the statistical analysis is carried out. Those obtained results may be useful for understanding the essence of uncertainty for a FPIS.

Keywords:

• Fuzzy relation
• FPIS
• uncertainty
• measure
• information granulation
• entropy

Acknowledgments

The authors would like to thank the editors and the anonymous reviewers for their valuable comments and suggestions, which have helped immensely in improving the quality of the paper.

Disclosure statement

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

Additional information

Funding

This work is supported by Natural Science Foundation of Guangxi (2018GXNSFAA294134) and Given Point on Master of Applied Statistics in Guangxi University of Finance and Economics (2016TJYB03).

Notes on contributors

Guangji Yu

Guangji Yu received the M. Sc. degree in Mathematics from Guangxi University, Nanning, China, in 1994. He is currently a professor in Guangxi Key Laboratory of Cross-border E-commerce Intelligent Information Processing. His research interests include rough set theory, fuzzy set theory and information systems.