Quantification of R-Fuzzy sets

Singh Khuman, Arjab and Yang, Yingjie and John, Robert (2016) Quantification of R-Fuzzy sets. Expert Systems with Applications, 55 . pp. 374-387. ISSN 0957-4174

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Abstract

The main aim of this paper is to connect R-Fuzzy sets and type-2 fuzzy sets, so as to provide a practical means to express complex uncertainty without the associated difficulty of a type-2 fuzzy set. The paper puts forward a significance measure, to provide a means for understanding the importance of the membership values contained within an R-fuzzy set. The pairing of an R-fuzzy set and the significance measure allows for an intermediary approach to that of a type-2 fuzzy set. By inspecting the returned significance degree of a particular membership value, one is able to ascertain its true significance in relation, relative to other encapsulated membership values. An R-fuzzy set coupled with the proposed significance measure allows for a type-2 fuzzy equivalence, an intermediary, all the while retaining the underlying sentiment of individual and general perspectives, and with the adage of a significantly reduced computational burden. Several human based perception examples are presented, wherein the significance degree is implemented, from which a higher level of detail can be garnered. The results demonstrate that the proposed research method combines the high capacity in uncertainty representation of type-2 fuzzy sets, together with the simplicity and objectiveness of type-1 fuzzy sets. This in turn provides a practical means for problem domains where a type-2 fuzzy set is preferred but difficult to construct due to the subjective type-2 fuzzy membership.

Item Type: Article
Keywords: R-Fuzzy Sets, Rough Sets, Fuzzy Membership, Significance, Type-2 Equivalence
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Computer Science
Identification Number: https://doi.org/10.1016/j.eswa.2016.02.010
Related URLs:
URLURL Type
http://www.sciencedirect.com/science/journal/09574174/44UNSPECIFIED
Depositing User: John, Professor Robert
Date Deposited: 12 Feb 2016 14:08
Last Modified: 22 Sep 2016 10:14
URI: http://eprints.nottingham.ac.uk/id/eprint/31652

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