Uncertainty Measurement for a Fuzzy Relation Information System

A fuzzy relation information system may be viewed as an information system with fuzzy relations. Uncertainty measurement is a critical evaluating tool. This paper investigates uncertainty measurement for a fuzzy relation information system. The concept of information structures in a fuzzy relation i...

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Bibliographic Details
Published in:IEEE transactions on fuzzy systems 2019-12, Vol.27 (12), p.2338-2352
Main Authors: Li, Zhaowen, Zhang, Pengfei, Ge, Xun, Xie, Ningxin, Zhang, Gangqiang, Wen, Ching-Feng
Format: Article
Language:English
Subjects:
Characterization
effectiveness
Entropy
Entropy (Information theory)
fuzzy relation
fuzzy relation information system
Fuzzy sets
Fuzzy systems
granularity
Granulation
Homomorphisms
information structure
Information systems
Knowledge based systems
measurement
Rough sets
Uncertainty
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Summary:A fuzzy relation information system may be viewed as an information system with fuzzy relations. Uncertainty measurement is a critical evaluating tool. This paper investigates uncertainty measurement for a fuzzy relation information system. The concept of information structures in a fuzzy relation information system is first described by using set vectors. Then, dependence between information structures in a fuzzy relation information system is given. Next, the axiom definition of the granularity measurement of the uncertainty for fuzzy relation information systems is proposed by means of its information structures. Based upon this axiom definition, information granulation and rough entropy in a fuzzy relation information system are proposed. Moreover, information entropy, information amount, joint entropy, and condition entropy in a fuzzy relation information system are also considered. To show the feasibility of the proposed measures for uncertainty of a fuzzy relation information system, effectiveness analysis is conducted from the angle of statistics. Finally, characterizations of fuzzy relation information systems under a compatible homomorphism are obtained. These results will be helpful for understanding the essence of uncertainty in a fuzzy relation information system.
ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2019.2898158