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We work only with tree networks and we assume that a minimum cost spanning tree network has already been constructed and now we are interested in the maintenance costs. The classic problem supposes that each agent stays for the entire time in the same node of the network. This paper introduces cost-allocation problems in a fixed-tree network with a set of agents whose activity over the nodes is fuzzy. Agent\u2019s needs to pay for each period of time may differ. Moreover, the agents do not always remain in the same node for each period. We propose the extension of a very well-known solution for these problems: Bird\u2019s rule.\n\n<\/jats:p>","DOI":"10.1007\/s10700-021-09375-8","type":"journal-article","created":{"date-parts":[[2022,1,10]],"date-time":"2022-01-10T07:03:07Z","timestamp":1641798187000},"page":"531-551","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Cost-allocation problems for fuzzy agents in a fixed-tree network"],"prefix":"10.1007","volume":"21","author":[{"given":"Julio R.","family":"Fern\u00e1ndez","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"In\u00e9s","family":"Gallego","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7571-1240","authenticated-orcid":false,"given":"Andr\u00e9s","family":"Jim\u00e9nez-Losada","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Manuel","family":"Ord\u00f3\u00f1ez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,1,10]]},"reference":[{"key":"9375_CR1","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1007\/s00199-009-0444-2","volume":"43","author":"G Berganti\u00f1os","year":"2010","unstructured":"Berganti\u00f1os, G., & G\u00f3mez-R\u00faa, M. 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