Measures of uncertainty for a distributed fully fuzzy information system

ABSTRACT

As an important model in the field of artificial intelligence, an information system is a database that stands for relationships between objects and attributes. A distributed fully fuzzy information system is an information system with distributed fully fuzzy data. This paper investigates measures of uncertainty for a distributed fully fuzzy information system. The fuzzy $T_{\cos }$-equivalence relation, induced by a fully fuzzy information system by using Gaussian kernel method, is first obtained. Then, fuzzy information structures in a distributed fully fuzzy information system is introduced. Next, Dependency between fuzzy information structures is depicted from three aspects, information distance for calculating the difference between fuzzy information structures is proposed in the same distributed fully fuzzy information system. Moreover, properties of fuzzy information structures in a distributed fully fuzzy information system are given by means of the inclusion degree. Finally, granulation measure and entropy measure of a given distributed fully fuzzy information system is proposed by means of its fuzzy information structures. These results will be very helpful for establishing a framework of granular computing and understanding the essence of uncertainty in distributed fully fuzzy information systems.

KEYWORDS:

• Distributed fully fuzzy information system
• fuzzy information structure
• dependence
• information distance
• inclusion degree
• uncertainty
• measure
• granulation
• entropy

Acknowledgements

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 authors.

Additional information

Funding

This work is supported by High Level Innovation Team Program from Guangxi Higher Education Institutions of China (Document No. [2018] 35), Natural Science Foundation of Guangxi (2018GXNSFDA294003, 2018GXNSFDA281028, 2018GXNSFAA294134), Key Laboratory of Software Engineering in Guangxi University for Nationalities (2018-18XJSY-03), Engineering Project of Undergraduate Teaching Reform of Higher Education in Guangxi (2017JGA179) and Research Project of Data Research Institute in Yulin (2019YJKY03).

Notes on contributors

Xiaofeng Liu

Xiaofeng Liu received the M. Sc. degree in Mathematics from Guangxi University for Nationalities, Nanning, China, in 2018. He is currently a doctoral student in School of Mathematics and Statistics, Hunan Normal University. Her main research interests include rough set theory and information system.

Zhaowen Li

Zhaowen Li received the M. Sc. degree in Mathematics from Guangxi University, Nanning, China, in 1988 and the Ph.D. degree in Mathematics from Hunan University, Changsha, China, in 2008. He is currently a professor in School of Mathematics and Statistics, Yulin Normal University. His research interests include topology and its applications, rough set theory, soft set theory, fuzzy set theory and information system.

Gangqiang Zhang

Gangqiang Zhang received the M. Sc. degree in Software Engineering from Beihang University, Beijing, China, in 2006. He is currently a associate professor in School of Software and Information Security, Guangxi University for Nationalities. His main research interests include rough set theory, fuzzy set theory and information system.

Ningxin Xie

Ningxin Xie received the M. Sc. degree in Computer from Guangxi University, Nanning, China, in 2001. He is currently a associate professor in School of Software and Information Security, Guangxi University for Nationalities. His main research interests include rough set theory, fuzzy set theory and information system.