Reducing fuzzy relation equations via concept lattices
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914967869980672 |
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| author | Lobo, David López-Marchante, Víctor Medina, Jesús |
| author_facet | Lobo, David López-Marchante, Víctor Medina, Jesús |
| contents | This paper has taken into advantage the relationship between Fuzzy Relation Equations (FRE) and Concept Lattices in order to introduce a procedure to reduce a FRE, without losing information. Specifically, attribute reduction theory in property-oriented and object-oriented concept lattices has been considered in order to present a mechanism for detecting redundant equations. As a first consequence, the computation of the whole solution set of a solvable FRE is reduced. Moreover, we will also introduce a novel method for computing approximate solutions of unsolvable FRE related to a (real) dataset with uncertainty/imprecision data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05728 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reducing fuzzy relation equations via concept lattices Lobo, David López-Marchante, Víctor Medina, Jesús Artificial Intelligence This paper has taken into advantage the relationship between Fuzzy Relation Equations (FRE) and Concept Lattices in order to introduce a procedure to reduce a FRE, without losing information. Specifically, attribute reduction theory in property-oriented and object-oriented concept lattices has been considered in order to present a mechanism for detecting redundant equations. As a first consequence, the computation of the whole solution set of a solvable FRE is reduced. Moreover, we will also introduce a novel method for computing approximate solutions of unsolvable FRE related to a (real) dataset with uncertainty/imprecision data. |
| title | Reducing fuzzy relation equations via concept lattices |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2410.05728 |