Construction of Fuzzy Measures over Product Spaces
In this paper, we study the problem of constructing a fuzzy measure over a product space when fuzzy measures over the marginal spaces are available. We propose a definition of independence of fuzzy measures and introduce different ways of constructing product measures, analyzing their properties. We...
| Main Authors: | , , |
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
| Published: |
MDPI
2020
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10835/8477 |
| _version_ | 1789406756667916288 |
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| author | Reche Lorite, Fernando Morales Giraldo, María Encarnación Salmerón Cerdán, Antonio |
| author_facet | Reche Lorite, Fernando Morales Giraldo, María Encarnación Salmerón Cerdán, Antonio |
| author_sort | Reche Lorite, Fernando |
| collection | DSpace |
| description | In this paper, we study the problem of constructing a fuzzy measure over a product space when fuzzy measures over the marginal spaces are available. We propose a definition of independence of fuzzy measures and introduce different ways of constructing product measures, analyzing their properties. We derive bounds for the measure on the product space and show that it is possible to construct a single product measure when the marginal measures are capacities of order 2. We also study the combination of real functions over the marginal spaces in order to produce a joint function over the product space, compatible with the concept of marginalization, paving the way for the definition of statistical indices based on fuzzy measures. |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-8477 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2020 |
| publisher | MDPI |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-84772023-12-15T13:26:02Z Construction of Fuzzy Measures over Product Spaces Reche Lorite, Fernando Morales Giraldo, María Encarnación Salmerón Cerdán, Antonio fuzzy measures monotone measures product spaces In this paper, we study the problem of constructing a fuzzy measure over a product space when fuzzy measures over the marginal spaces are available. We propose a definition of independence of fuzzy measures and introduce different ways of constructing product measures, analyzing their properties. We derive bounds for the measure on the product space and show that it is possible to construct a single product measure when the marginal measures are capacities of order 2. We also study the combination of real functions over the marginal spaces in order to produce a joint function over the product space, compatible with the concept of marginalization, paving the way for the definition of statistical indices based on fuzzy measures. 2020-09-28T07:08:55Z 2020-09-28T07:08:55Z 2020-09-17 info:eu-repo/semantics/article 2227-7390 http://hdl.handle.net/10835/8477 en https://www.mdpi.com/2227-7390/8/9/1605 Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess MDPI |
| spellingShingle | fuzzy measures monotone measures product spaces Reche Lorite, Fernando Morales Giraldo, María Encarnación Salmerón Cerdán, Antonio Construction of Fuzzy Measures over Product Spaces |
| title | Construction of Fuzzy Measures over Product Spaces |
| title_full | Construction of Fuzzy Measures over Product Spaces |
| title_fullStr | Construction of Fuzzy Measures over Product Spaces |
| title_full_unstemmed | Construction of Fuzzy Measures over Product Spaces |
| title_short | Construction of Fuzzy Measures over Product Spaces |
| title_sort | construction of fuzzy measures over product spaces |
| topic | fuzzy measures monotone measures product spaces |
| url | http://hdl.handle.net/10835/8477 |
| work_keys_str_mv | AT recheloritefernando constructionoffuzzymeasuresoverproductspaces AT moralesgiraldomariaencarnacion constructionoffuzzymeasuresoverproductspaces AT salmeroncerdanantonio constructionoffuzzymeasuresoverproductspaces |