Quantification of R-Fuzzy sets
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 o...
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| Format: | Article |
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Elsevier
2016
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| Online Access: | https://eprints.nottingham.ac.uk/31652/ |
| _version_ | 1848794245508366336 |
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| author | Singh Khuman, Arjab Yang, Yingjie John, Robert |
| author_facet | Singh Khuman, Arjab Yang, Yingjie John, Robert |
| author_sort | Singh Khuman, Arjab |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:13:08Z |
| format | Article |
| id | nottingham-31652 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:13:08Z |
| publishDate | 2016 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-316522020-05-04T18:07:00Z https://eprints.nottingham.ac.uk/31652/ Quantification of R-Fuzzy sets Singh Khuman, Arjab Yang, Yingjie John, Robert 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. Elsevier 2016-08-15 Article PeerReviewed Singh Khuman, Arjab, Yang, Yingjie and John, Robert (2016) Quantification of R-Fuzzy sets. Expert Systems with Applications, 55 . pp. 374-387. ISSN 0957-4174 R-Fuzzy Sets Rough Sets Fuzzy Membership Significance Type-2 Equivalence http://www.sciencedirect.com/science/article/pii/S0957417416300331 doi:10.1016/j.eswa.2016.02.010 doi:10.1016/j.eswa.2016.02.010 |
| spellingShingle | R-Fuzzy Sets Rough Sets Fuzzy Membership Significance Type-2 Equivalence Singh Khuman, Arjab Yang, Yingjie John, Robert Quantification of R-Fuzzy sets |
| title | Quantification of R-Fuzzy sets |
| title_full | Quantification of R-Fuzzy sets |
| title_fullStr | Quantification of R-Fuzzy sets |
| title_full_unstemmed | Quantification of R-Fuzzy sets |
| title_short | Quantification of R-Fuzzy sets |
| title_sort | quantification of r-fuzzy sets |
| topic | R-Fuzzy Sets Rough Sets Fuzzy Membership Significance Type-2 Equivalence |
| url | https://eprints.nottingham.ac.uk/31652/ https://eprints.nottingham.ac.uk/31652/ https://eprints.nottingham.ac.uk/31652/ |