Quantification of R-Fuzzy sets

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

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.

Citation

Singh Khuman, A., Yang, Y., & John, R. (2016). Quantification of R-Fuzzy sets. Expert Systems with Applications, 55, https://doi.org/10.1016/j.eswa.2016.02.010

• Journal Article Type: Article
• Acceptance Date: Feb 7, 2016
• Online Publication Date: Feb 20, 2016
• Publication Date: Aug 15, 2016
• Deposit Date: Feb 12, 2016
• Publicly Available Date: Feb 20, 2016
• Journal: Expert Systems with Applications
• Print ISSN: 0957-4174
• Electronic ISSN: 0957-4174
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 55
• DOI: https://doi.org/10.1016/j.eswa.2016.02.010
• Keywords: R-Fuzzy Sets, Rough Sets, Fuzzy Membership, Significance, Type-2 Equivalence
• Public URL: https://nottingham-repository.worktribe.com/output/805632
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0957417416300331
• Related Public URLs: http://www.sciencedirect.com/science/journal/09574174/44