Operation properties and δ-equalities of complex fuzzy sets
A complex fuzzy set is a fuzzy set whose membership function takes values in the unit circle in the complex plane. This paper investigates various operation properties and proposes a distance measure for complex fuzzy sets. The distance of two complex fuzzy sets measures the difference between the g...
| Main Authors: | , , , , |
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| Format: | Journal Article |
| Published: |
Elsevier
2009
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/26238 |
| _version_ | 1848751929329451008 |
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| author | Zhang, G. Dillon, Tharam S Cai, K. Ma, J. Lu, J. |
| author_facet | Zhang, G. Dillon, Tharam S Cai, K. Ma, J. Lu, J. |
| author_sort | Zhang, G. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | A complex fuzzy set is a fuzzy set whose membership function takes values in the unit circle in the complex plane. This paper investigates various operation properties and proposes a distance measure for complex fuzzy sets. The distance of two complex fuzzy sets measures the difference between the grades of two complex fuzzy sets as well as that between the phases of the two complex fuzzy sets. This distance measure is then used to define equalities of complex fuzzy sets which coincide with those of fuzzy sets already defined in the literature if complex fuzzy sets reduce to real-valued fuzzy sets. Two complex fuzzy sets are said to be d-equal if the distance between them is less than 1 d. This paper shows how various operations between complex fuzzy sets affect given δ-equalities of complex fuzzy sets. An example application of signal detection demonstrates the utility of the concept of δ-equalities of complex fuzzy sets in practice. |
| first_indexed | 2025-11-14T08:00:32Z |
| format | Journal Article |
| id | curtin-20.500.11937-26238 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:00:32Z |
| publishDate | 2009 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-262382017-09-13T15:56:21Z Operation properties and δ-equalities of complex fuzzy sets Zhang, G. Dillon, Tharam S Cai, K. Ma, J. Lu, J. operation fuzzy set Complex fuzzy set distance measure a-equality A complex fuzzy set is a fuzzy set whose membership function takes values in the unit circle in the complex plane. This paper investigates various operation properties and proposes a distance measure for complex fuzzy sets. The distance of two complex fuzzy sets measures the difference between the grades of two complex fuzzy sets as well as that between the phases of the two complex fuzzy sets. This distance measure is then used to define equalities of complex fuzzy sets which coincide with those of fuzzy sets already defined in the literature if complex fuzzy sets reduce to real-valued fuzzy sets. Two complex fuzzy sets are said to be d-equal if the distance between them is less than 1 d. This paper shows how various operations between complex fuzzy sets affect given δ-equalities of complex fuzzy sets. An example application of signal detection demonstrates the utility of the concept of δ-equalities of complex fuzzy sets in practice. 2009 Journal Article http://hdl.handle.net/20.500.11937/26238 10.1016/j.ijar.2009.05.010 Elsevier fulltext |
| spellingShingle | operation fuzzy set Complex fuzzy set distance measure a-equality Zhang, G. Dillon, Tharam S Cai, K. Ma, J. Lu, J. Operation properties and δ-equalities of complex fuzzy sets |
| title | Operation properties and δ-equalities of complex fuzzy sets |
| title_full | Operation properties and δ-equalities of complex fuzzy sets |
| title_fullStr | Operation properties and δ-equalities of complex fuzzy sets |
| title_full_unstemmed | Operation properties and δ-equalities of complex fuzzy sets |
| title_short | Operation properties and δ-equalities of complex fuzzy sets |
| title_sort | operation properties and δ-equalities of complex fuzzy sets |
| topic | operation fuzzy set Complex fuzzy set distance measure a-equality |
| url | http://hdl.handle.net/20.500.11937/26238 |