SPFI: shape-preserving Choquet fuzzy integral for non-normal fuzzy set-valued evidence
Information or data aggregation is an important part of nearly all analysis problems as summarizing inputs from multiple sources is a ubiquitous goal. In this paper we propose a method for non-linear aggregation of data inputs that take the form of non-normal fuzzy sets. The proposed shape-preservin...
| Main Authors: | , , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
2018
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| Online Access: | https://eprints.nottingham.ac.uk/53458/ |
| _version_ | 1848798944636698624 |
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| author | Havens, Timothy C. Pinar, Anthony J. Anderson, Derek T. Wagner, Christian |
| author_facet | Havens, Timothy C. Pinar, Anthony J. Anderson, Derek T. Wagner, Christian |
| author_sort | Havens, Timothy C. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Information or data aggregation is an important part of nearly all analysis problems as summarizing inputs from multiple sources is a ubiquitous goal. In this paper we propose a method for non-linear aggregation of data inputs that take the form of non-normal fuzzy sets. The proposed shape-preserving fuzzy integral (SPFI) is designed to overcome a well-known weakness of the previously-proposed sub-normal fuzzy integral (SuFI). The weakness of SuFI is that the output is constrained to have maximum membership equal to the minimum of the maximum memberships of the inputs; hence, if one input has a small height, then the output is constrained to that height. The proposed SPFI does not suffer from this weakness and, furthermore, preserves in the output the shape of the input sets. That is, the output looks like the inputs. The SPFI method is based on the well-known Choquet fuzzy integral with respect to a capacity measure, i.e., fuzzy measure. We demonstrate SPFI on synthetic and real-world data, comparing it to the SuFI and non-direct fuzzy integral (NDFI). |
| first_indexed | 2025-11-14T20:27:49Z |
| format | Conference or Workshop Item |
| id | nottingham-53458 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:27:49Z |
| publishDate | 2018 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-534582018-08-24T13:00:42Z https://eprints.nottingham.ac.uk/53458/ SPFI: shape-preserving Choquet fuzzy integral for non-normal fuzzy set-valued evidence Havens, Timothy C. Pinar, Anthony J. Anderson, Derek T. Wagner, Christian Information or data aggregation is an important part of nearly all analysis problems as summarizing inputs from multiple sources is a ubiquitous goal. In this paper we propose a method for non-linear aggregation of data inputs that take the form of non-normal fuzzy sets. The proposed shape-preserving fuzzy integral (SPFI) is designed to overcome a well-known weakness of the previously-proposed sub-normal fuzzy integral (SuFI). The weakness of SuFI is that the output is constrained to have maximum membership equal to the minimum of the maximum memberships of the inputs; hence, if one input has a small height, then the output is constrained to that height. The proposed SPFI does not suffer from this weakness and, furthermore, preserves in the output the shape of the input sets. That is, the output looks like the inputs. The SPFI method is based on the well-known Choquet fuzzy integral with respect to a capacity measure, i.e., fuzzy measure. We demonstrate SPFI on synthetic and real-world data, comparing it to the SuFI and non-direct fuzzy integral (NDFI). 2018-07-08 Conference or Workshop Item PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/53458/1/spfi-shape-preserving.pdf Havens, Timothy C., Pinar, Anthony J., Anderson, Derek T. and Wagner, Christian (2018) SPFI: shape-preserving Choquet fuzzy integral for non-normal fuzzy set-valued evidence. In: IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2018), 8-12 Jul 2018, Rio de Janeiro, Brazil. |
| spellingShingle | Havens, Timothy C. Pinar, Anthony J. Anderson, Derek T. Wagner, Christian SPFI: shape-preserving Choquet fuzzy integral for non-normal fuzzy set-valued evidence |
| title | SPFI: shape-preserving Choquet fuzzy integral for non-normal fuzzy set-valued evidence |
| title_full | SPFI: shape-preserving Choquet fuzzy integral for non-normal fuzzy set-valued evidence |
| title_fullStr | SPFI: shape-preserving Choquet fuzzy integral for non-normal fuzzy set-valued evidence |
| title_full_unstemmed | SPFI: shape-preserving Choquet fuzzy integral for non-normal fuzzy set-valued evidence |
| title_short | SPFI: shape-preserving Choquet fuzzy integral for non-normal fuzzy set-valued evidence |
| title_sort | spfi: shape-preserving choquet fuzzy integral for non-normal fuzzy set-valued evidence |
| url | https://eprints.nottingham.ac.uk/53458/ |