Some Properties of the Extended Threshold Generated Implications
Fuzzy implications play an important role in both approximating reasoning and fuzzy control, and there are many generation methods for fuzzy implications for various applications. The extended threshold generation method for fuzzy implications can induce some implications differ from the usual impli...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Tsinghua University Press
2024-09-01
|
| Series: | Fuzzy Information and Engineering |
| Subjects: | |
| Online Access: | https://www.sciopen.com/article/10.26599/FIE.2024.9270040 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850266247601586176 |
|---|---|
| author | Zhi-Hong Yi Li-Juan Yao Feng Qin |
| author_facet | Zhi-Hong Yi Li-Juan Yao Feng Qin |
| author_sort | Zhi-Hong Yi |
| collection | DOAJ |
| description | Fuzzy implications play an important role in both approximating reasoning and fuzzy control, and there are many generation methods for fuzzy implications for various applications. The extended threshold generation method for fuzzy implications can induce some implications differ from the usual implications, such as f-, g-implications, R-implications, S-implications, and those derived from the ordinal sum method. In this paper, we focus on the investigations of the preservation of some important properties under minimal necessary conditions similar to the e-threshold generation method, such as the neutral property, the exchange law, the weak importation law, the contraction law, and the distributivity property over t-norms and t-conorms. |
| format | Article |
| id | doaj-art-e211786c582d483a984c7ef793522b9b |
| institution | OA Journals |
| issn | 1616-8658 1616-8666 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | Tsinghua University Press |
| record_format | Article |
| series | Fuzzy Information and Engineering |
| spelling | doaj-art-e211786c582d483a984c7ef793522b9b2025-08-20T01:54:12ZengTsinghua University PressFuzzy Information and Engineering1616-86581616-86662024-09-0116317519310.26599/FIE.2024.9270040Some Properties of the Extended Threshold Generated ImplicationsZhi-Hong Yi0Li-Juan Yao1Feng Qin2College of Mathematics and Information Science, Nanchang Normal University, Nanchang 330032, ChinaCollege of Mathematics and Information Science, Nanchang Normal University, Nanchang 330032, ChinaCollege of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, ChinaFuzzy implications play an important role in both approximating reasoning and fuzzy control, and there are many generation methods for fuzzy implications for various applications. The extended threshold generation method for fuzzy implications can induce some implications differ from the usual implications, such as f-, g-implications, R-implications, S-implications, and those derived from the ordinal sum method. In this paper, we focus on the investigations of the preservation of some important properties under minimal necessary conditions similar to the e-threshold generation method, such as the neutral property, the exchange law, the weak importation law, the contraction law, and the distributivity property over t-norms and t-conorms.https://www.sciopen.com/article/10.26599/FIE.2024.9270040fuzzy implicationsextended threshold generationexchange principlelaw of importationcontraction lawdistributivity property |
| spellingShingle | Zhi-Hong Yi Li-Juan Yao Feng Qin Some Properties of the Extended Threshold Generated Implications Fuzzy Information and Engineering fuzzy implications extended threshold generation exchange principle law of importation contraction law distributivity property |
| title | Some Properties of the Extended Threshold Generated Implications |
| title_full | Some Properties of the Extended Threshold Generated Implications |
| title_fullStr | Some Properties of the Extended Threshold Generated Implications |
| title_full_unstemmed | Some Properties of the Extended Threshold Generated Implications |
| title_short | Some Properties of the Extended Threshold Generated Implications |
| title_sort | some properties of the extended threshold generated implications |
| topic | fuzzy implications extended threshold generation exchange principle law of importation contraction law distributivity property |
| url | https://www.sciopen.com/article/10.26599/FIE.2024.9270040 |
| work_keys_str_mv | AT zhihongyi somepropertiesoftheextendedthresholdgeneratedimplications AT lijuanyao somepropertiesoftheextendedthresholdgeneratedimplications AT fengqin somepropertiesoftheextendedthresholdgeneratedimplications |