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R-fuzzy sets and grey system theory

Singh Khuman, Arjab; Yang, Yingjie; John, Robert; Liu, Sifeng


Arjab Singh Khuman

Yingjie Yang

Robert John

Sifeng Liu


This paper investigates the use of grey theory to en- hance the concept of an R-fuzzy set, with regards to the precision of the encapsulating set of returned significance values. The use of lower and upper approximations from rough set theory, allow for an R-fuzzy approach to encapsulate uncertain fuzzy membership values; both collectively generic and individually specific. The authors have previously created a significance measure, which when combined with an R-fuzzy set provides one with a refined approach for expressing complex uncertainty. This pairing of an R-fuzzy set and the significance measure, replicates in part, the high detail of uncertainty representation from a type-2 fuzzy approach, with the relative ease and objectiveness of a type-1 fuzzy approach. As a result, this new research method allows for a practical means for domains where ideally a generalised type-2 fuzzy set is more favourable, but ultimately unfeasible due to the subjectiveness of type-2 fuzzy membership values. This paper focuses on providing a more effective means for the creation of the set which encapsulates the returned degrees of significance. Using grey techniques, rather than the arbitrary configuration of the original work, the result is a high precision set for encapsulation, with the minimal configuration of parameter values. A worked example is used to demonstrate the effectiveness of using grey theory in conjunction with R-fuzzy sets and the significance measure.


Singh Khuman, A., Yang, Y., John, R., & Liu, S. (2017). R-fuzzy sets and grey system theory. In 2016 IEEE International Conference on Systems, Man, and Cybernetics (SMC).

Conference Name 2016 IEEE International Conference on Systems, Man, and Cybernetics (SMC 2016)
Start Date Oct 9, 2016
End Date Oct 12, 2016
Acceptance Date Jun 1, 2016
Publication Date Feb 9, 2017
Deposit Date Jun 8, 2016
Publicly Available Date Feb 9, 2017
Peer Reviewed Peer Reviewed
Book Title 2016 IEEE International Conference on Systems, Man, and Cybernetics (SMC)
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