An Algorithm for Producing Fuzzy Implications via Conical Sections
In the present study, a novel parametric family of fuzzy implications is introduced and its properties are examined. The parametric family of implications is produced only via a fuzzy negation. This in turn enables the effortless production of a wide range of implications from which to select the on...
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MDPI AG
2024-11-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/17/11/499 |
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| author | Ioannis Karampinis Georgios Souliotis Basil Papadopoulos Athanasios Karabinis |
| author_facet | Ioannis Karampinis Georgios Souliotis Basil Papadopoulos Athanasios Karabinis |
| author_sort | Ioannis Karampinis |
| collection | DOAJ |
| description | In the present study, a novel parametric family of fuzzy implications is introduced and its properties are examined. The parametric family of implications is produced only via a fuzzy negation. This in turn enables the effortless production of a wide range of implications from which to select the one that best fits a given problem, for example in fuzzy inference systems or fuzzy neural networks. The fuzzy negations that have been selected as a basis for the proposed methodology are strong, i.e., involutions, thus leading, in general, to the generated fuzzy implications possessing many desirable additional properties. We have examined which of these properties hold for the implications produced by our algorithm and under which conditions. Finally, it is demonstrated that the family of implications generated via the proposed methodology generalizes other well-established implications, including the Łukasiewicz implication. |
| format | Article |
| id | doaj-art-94f78c8f6a20460ea5cb6dda64cb0baa |
| institution | Kabale University |
| issn | 1999-4893 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj-art-94f78c8f6a20460ea5cb6dda64cb0baa2024-11-26T17:45:25ZengMDPI AGAlgorithms1999-48932024-11-01171149910.3390/a17110499An Algorithm for Producing Fuzzy Implications via Conical SectionsIoannis Karampinis0Georgios Souliotis1Basil Papadopoulos2Athanasios Karabinis3Laboratory of Mathematics and Informatics, Department of Civil Engineering, Democritus University of Thrace, 67100 Kimeria, GreeceLaboratory of Mathematics and Informatics, Department of Civil Engineering, Democritus University of Thrace, 67100 Kimeria, GreeceLaboratory of Mathematics and Informatics, Department of Civil Engineering, Democritus University of Thrace, 67100 Kimeria, GreeceLaboratory of Reinforced Concrete and Seismic Design, Department of Civil Engineering, Democritus University of Thrace, 67100 Xanthi, GreeceIn the present study, a novel parametric family of fuzzy implications is introduced and its properties are examined. The parametric family of implications is produced only via a fuzzy negation. This in turn enables the effortless production of a wide range of implications from which to select the one that best fits a given problem, for example in fuzzy inference systems or fuzzy neural networks. The fuzzy negations that have been selected as a basis for the proposed methodology are strong, i.e., involutions, thus leading, in general, to the generated fuzzy implications possessing many desirable additional properties. We have examined which of these properties hold for the implications produced by our algorithm and under which conditions. Finally, it is demonstrated that the family of implications generated via the proposed methodology generalizes other well-established implications, including the Łukasiewicz implication.https://www.mdpi.com/1999-4893/17/11/499fuzzy implicationsfuzzy negationstrong fuzzy negation |
| spellingShingle | Ioannis Karampinis Georgios Souliotis Basil Papadopoulos Athanasios Karabinis An Algorithm for Producing Fuzzy Implications via Conical Sections Algorithms fuzzy implications fuzzy negation strong fuzzy negation |
| title | An Algorithm for Producing Fuzzy Implications via Conical Sections |
| title_full | An Algorithm for Producing Fuzzy Implications via Conical Sections |
| title_fullStr | An Algorithm for Producing Fuzzy Implications via Conical Sections |
| title_full_unstemmed | An Algorithm for Producing Fuzzy Implications via Conical Sections |
| title_short | An Algorithm for Producing Fuzzy Implications via Conical Sections |
| title_sort | algorithm for producing fuzzy implications via conical sections |
| topic | fuzzy implications fuzzy negation strong fuzzy negation |
| url | https://www.mdpi.com/1999-4893/17/11/499 |
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