Data-informed fuzzy measures for fuzzy integration of intervals and fuzzy numbers
The fuzzy integral (FI) with respect to a fuzzy measure (FM) is a powerful means of aggregating information. The most popular FIs are the Choquet and Sugeno, and most research focuses on these two variants. The arena of the FM is much more populated, including numerically derived FMs such as the Sug...
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IEEE
2015
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| Online Access: | https://eprints.nottingham.ac.uk/37872/ |
| _version_ | 1848795552035110912 |
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| author | Havens, Timothy C. Anderson, Derek T. Wagner, Christian |
| author_facet | Havens, Timothy C. Anderson, Derek T. Wagner, Christian |
| author_sort | Havens, Timothy C. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | The fuzzy integral (FI) with respect to a fuzzy measure (FM) is a powerful means of aggregating information. The most popular FIs are the Choquet and Sugeno, and most research focuses on these two variants. The arena of the FM is much more populated, including numerically derived FMs such as the Sugeno λ-measure and decomposable measure, expert-defined FMs, and data-informed FMs. The drawback of numerically derived and expert-defined FMs is that one must know something about the relative values of the input sources. However, there are many problems where this information is unavailable, such as crowdsourcing. This paper focuses on data-informed FMs, or those FMs that are computed by an algorithm that analyzes some property of the input data itself, gleaning the importance of each input source by the data they provide. The original instantiation of a data-informed FM is the agreement FM, which assigns high confidence to combinations of sources that numerically agree with one another. This paper extends upon our previous work in datainformed FMs by proposing the uniqueness measure and additive measure of agreement for interval-valued evidence. We then extend data-informed FMs to fuzzy number (FN)-valued inputs. We demonstrate the proposed FMs by aggregating interval and FN evidence with the Choquet and Sugeno FIs for both synthetic and real-world data. |
| first_indexed | 2025-11-14T19:33:54Z |
| format | Article |
| id | nottingham-37872 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:33:54Z |
| publishDate | 2015 |
| publisher | IEEE |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-378722020-05-04T20:06:57Z https://eprints.nottingham.ac.uk/37872/ Data-informed fuzzy measures for fuzzy integration of intervals and fuzzy numbers Havens, Timothy C. Anderson, Derek T. Wagner, Christian The fuzzy integral (FI) with respect to a fuzzy measure (FM) is a powerful means of aggregating information. The most popular FIs are the Choquet and Sugeno, and most research focuses on these two variants. The arena of the FM is much more populated, including numerically derived FMs such as the Sugeno λ-measure and decomposable measure, expert-defined FMs, and data-informed FMs. The drawback of numerically derived and expert-defined FMs is that one must know something about the relative values of the input sources. However, there are many problems where this information is unavailable, such as crowdsourcing. This paper focuses on data-informed FMs, or those FMs that are computed by an algorithm that analyzes some property of the input data itself, gleaning the importance of each input source by the data they provide. The original instantiation of a data-informed FM is the agreement FM, which assigns high confidence to combinations of sources that numerically agree with one another. This paper extends upon our previous work in datainformed FMs by proposing the uniqueness measure and additive measure of agreement for interval-valued evidence. We then extend data-informed FMs to fuzzy number (FN)-valued inputs. We demonstrate the proposed FMs by aggregating interval and FN evidence with the Choquet and Sugeno FIs for both synthetic and real-world data. IEEE 2015-10 Article PeerReviewed Havens, Timothy C., Anderson, Derek T. and Wagner, Christian (2015) Data-informed fuzzy measures for fuzzy integration of intervals and fuzzy numbers. IEEE Transactions on Fuzzy Systems, 23 (5). pp. 1861-1875. ISSN 1941-0034 Frequency modulation Indexes Density measurement Additives Educational institutions Equations Fuzzy sets http://ieeexplore.ieee.org/document/6987326/ doi:10.1109/TFUZZ.2014.2382133 doi:10.1109/TFUZZ.2014.2382133 |
| spellingShingle | Frequency modulation Indexes Density measurement Additives Educational institutions Equations Fuzzy sets Havens, Timothy C. Anderson, Derek T. Wagner, Christian Data-informed fuzzy measures for fuzzy integration of intervals and fuzzy numbers |
| title | Data-informed fuzzy measures for fuzzy integration of intervals and fuzzy numbers |
| title_full | Data-informed fuzzy measures for fuzzy integration of intervals and fuzzy numbers |
| title_fullStr | Data-informed fuzzy measures for fuzzy integration of intervals and fuzzy numbers |
| title_full_unstemmed | Data-informed fuzzy measures for fuzzy integration of intervals and fuzzy numbers |
| title_short | Data-informed fuzzy measures for fuzzy integration of intervals and fuzzy numbers |
| title_sort | data-informed fuzzy measures for fuzzy integration of intervals and fuzzy numbers |
| topic | Frequency modulation Indexes Density measurement Additives Educational institutions Equations Fuzzy sets |
| url | https://eprints.nottingham.ac.uk/37872/ https://eprints.nottingham.ac.uk/37872/ https://eprints.nottingham.ac.uk/37872/ |