On the Aggregation of Comonotone or Countermonotone Fuzzy Relations
The properties of fuzzy relations have been extensively studied, and the preservation of their properties plays a fundamental role in the various applications. However, either sufficient or necessity conditions for the preservation requires the aggregated functions of fuzzy relations to dominate or...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/5/958 |
| _version_ | 1797495134122672128 |
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| author | Yuanyuan Liu Fan Jia |
| author_facet | Yuanyuan Liu Fan Jia |
| author_sort | Yuanyuan Liu |
| collection | DOAJ |
| description | The properties of fuzzy relations have been extensively studied, and the preservation of their properties plays a fundamental role in the various applications. However, either sufficient or necessity conditions for the preservation requires the aggregated functions of fuzzy relations to dominate or to be dominated by the corresponding operations, which constructs a significant limitation on applicable functions. This work concentrates on the preservation of transitivities and Ferrers property for the aggregation of comonotone or countermonotone fuzzy relations. Firstly, definitions of comonotonicity and countermonotonicity for binary functions are initially proposed. On the foundation of that, the relations of commuting and bisymmetry between min/max and commonly used increasing/decreasing functions are found. Afterwards, with the condition that underlying fuzzy relations are pair-wisely comonotone or countermonotone, theorems on the aggregation functions which can preserve the transitivities and the Ferrers property are proposed. Moreover, an interesting conclusion that the equivalent condition for the min-Ferrers property of fuzzy relations is clarified. |
| first_indexed | 2024-03-10T01:44:06Z |
| format | Article |
| id | doaj.art-46bb811805654c638ee1523de5327709 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T01:44:06Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-46bb811805654c638ee1523de53277092023-11-23T13:18:57ZengMDPI AGSymmetry2073-89942022-05-0114595810.3390/sym14050958On the Aggregation of Comonotone or Countermonotone Fuzzy RelationsYuanyuan Liu0Fan Jia1School of Management Science and Engineering, Shangdong University of Finance and Economics, Jinan 250014, ChinaSchool of Management Science and Engineering, Shangdong University of Finance and Economics, Jinan 250014, ChinaThe properties of fuzzy relations have been extensively studied, and the preservation of their properties plays a fundamental role in the various applications. However, either sufficient or necessity conditions for the preservation requires the aggregated functions of fuzzy relations to dominate or to be dominated by the corresponding operations, which constructs a significant limitation on applicable functions. This work concentrates on the preservation of transitivities and Ferrers property for the aggregation of comonotone or countermonotone fuzzy relations. Firstly, definitions of comonotonicity and countermonotonicity for binary functions are initially proposed. On the foundation of that, the relations of commuting and bisymmetry between min/max and commonly used increasing/decreasing functions are found. Afterwards, with the condition that underlying fuzzy relations are pair-wisely comonotone or countermonotone, theorems on the aggregation functions which can preserve the transitivities and the Ferrers property are proposed. Moreover, an interesting conclusion that the equivalent condition for the min-Ferrers property of fuzzy relations is clarified.https://www.mdpi.com/2073-8994/14/5/958fuzzy relationaggregationcomonotonicitycountermonotonicitytransitivityferrers property |
| spellingShingle | Yuanyuan Liu Fan Jia On the Aggregation of Comonotone or Countermonotone Fuzzy Relations Symmetry fuzzy relation aggregation comonotonicity countermonotonicity transitivity ferrers property |
| title | On the Aggregation of Comonotone or Countermonotone Fuzzy Relations |
| title_full | On the Aggregation of Comonotone or Countermonotone Fuzzy Relations |
| title_fullStr | On the Aggregation of Comonotone or Countermonotone Fuzzy Relations |
| title_full_unstemmed | On the Aggregation of Comonotone or Countermonotone Fuzzy Relations |
| title_short | On the Aggregation of Comonotone or Countermonotone Fuzzy Relations |
| title_sort | on the aggregation of comonotone or countermonotone fuzzy relations |
| topic | fuzzy relation aggregation comonotonicity countermonotonicity transitivity ferrers property |
| url | https://www.mdpi.com/2073-8994/14/5/958 |
| work_keys_str_mv | AT yuanyuanliu ontheaggregationofcomonotoneorcountermonotonefuzzyrelations AT fanjia ontheaggregationofcomonotoneorcountermonotonefuzzyrelations |