Aggregation of Weak Fuzzy Norms
Aggregation is a mathematical process consisting in the fusion of a set of values into a unique one and representing them in some sense. Aggregation functions have demonstrated to be very important in many problems related to the fusion of information. This has resulted in the extended use of these...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/10/1908 |
| _version_ | 1797513092565827584 |
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| author | Tatiana Pedraza Jorge Ramos-Canós Jesús Rodríguez-López |
| author_facet | Tatiana Pedraza Jorge Ramos-Canós Jesús Rodríguez-López |
| author_sort | Tatiana Pedraza |
| collection | DOAJ |
| description | Aggregation is a mathematical process consisting in the fusion of a set of values into a unique one and representing them in some sense. Aggregation functions have demonstrated to be very important in many problems related to the fusion of information. This has resulted in the extended use of these functions not only to combine a family of numbers but also a family of certain mathematical structures such as metrics or norms, in the classical context, or indistinguishability operators or fuzzy metrics in the fuzzy context. In this paper, we study and characterize the functions through which we can obtain a single weak fuzzy (quasi-)norm from an arbitrary family of weak fuzzy (quasi-)norms in two different senses: when each weak fuzzy (quasi-)norm is defined on a possibly different vector space or when all of them are defined on the same vector space. We will show that, contrary to the crisp case, weak fuzzy (quasi-)norm aggregation functions are equivalent to fuzzy (quasi-)metric aggregation functions. |
| first_indexed | 2024-03-10T06:10:49Z |
| format | Article |
| id | doaj.art-cf6ddb53ab404663946d5aee02f04015 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T06:10:49Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-cf6ddb53ab404663946d5aee02f040152023-11-22T20:10:54ZengMDPI AGSymmetry2073-89942021-10-011310190810.3390/sym13101908Aggregation of Weak Fuzzy NormsTatiana Pedraza0Jorge Ramos-Canós1Jesús Rodríguez-López2Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, SpainInstituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, SpainInstituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, SpainAggregation is a mathematical process consisting in the fusion of a set of values into a unique one and representing them in some sense. Aggregation functions have demonstrated to be very important in many problems related to the fusion of information. This has resulted in the extended use of these functions not only to combine a family of numbers but also a family of certain mathematical structures such as metrics or norms, in the classical context, or indistinguishability operators or fuzzy metrics in the fuzzy context. In this paper, we study and characterize the functions through which we can obtain a single weak fuzzy (quasi-)norm from an arbitrary family of weak fuzzy (quasi-)norms in two different senses: when each weak fuzzy (quasi-)norm is defined on a possibly different vector space or when all of them are defined on the same vector space. We will show that, contrary to the crisp case, weak fuzzy (quasi-)norm aggregation functions are equivalent to fuzzy (quasi-)metric aggregation functions.https://www.mdpi.com/2073-8994/13/10/1908weak fuzzy quasi-normsaggregation function |
| spellingShingle | Tatiana Pedraza Jorge Ramos-Canós Jesús Rodríguez-López Aggregation of Weak Fuzzy Norms Symmetry weak fuzzy quasi-norms aggregation function |
| title | Aggregation of Weak Fuzzy Norms |
| title_full | Aggregation of Weak Fuzzy Norms |
| title_fullStr | Aggregation of Weak Fuzzy Norms |
| title_full_unstemmed | Aggregation of Weak Fuzzy Norms |
| title_short | Aggregation of Weak Fuzzy Norms |
| title_sort | aggregation of weak fuzzy norms |
| topic | weak fuzzy quasi-norms aggregation function |
| url | https://www.mdpi.com/2073-8994/13/10/1908 |
| work_keys_str_mv | AT tatianapedraza aggregationofweakfuzzynorms AT jorgeramoscanos aggregationofweakfuzzynorms AT jesusrodriguezlopez aggregationofweakfuzzynorms |