{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,17]],"date-time":"2025-04-17T14:48:16Z","timestamp":1744901296130},"reference-count":13,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[2009,4]]},"abstract":"<jats:p>The Cauchy equation for automorphisms of the unit interval is fulfilled only by the identity mapping. We consider two weakened forms of this Cauchy equation: the reciprocity equation and the n-divisibility equation. Although the solution sets of both functional equations are quite large, requiring that an automorphism is both reciprocal and n-divisible, drastically increases the set of obligatory fixed points. However, increasing n also enlarges the domain on which the automorphism can be chosen freely. We also describe the solution sets of two functional equations that arise by composing the reciprocity and n-divisibility property.<\/jats:p>","DOI":"10.1142\/s0218488509005826","type":"journal-article","created":{"date-parts":[[2009,3,27]],"date-time":"2009-03-27T11:19:21Z","timestamp":1238152761000},"page":"221-235","source":"Crossref","is-referenced-by-count":3,"title":["DIVISIBLE, RECIPROCAL AUTOMORPHISMS OF THE UNIT INTERVAL"],"prefix":"10.1142","volume":"17","author":[{"given":"KOEN C.","family":"MAES","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure Links 653, B-9000 Gent, Belgium"}]},{"given":"BERNARD","family":"DE BAETS","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure Links 653, B-9000 Gent, Belgium"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","first-page":"47","volume":"3","author":"Trillas E.","journal-title":"Stochastica"},{"key":"rf2","volume-title":"Trends in Logic","volume":"8","author":"Klement E.","year":"2000"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488597000312"},{"key":"rf4","first-page":"273","volume":"16","author":"Maes K.","journal-title":"J. Intelligent & Fuzzy Systems"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2006.880004"},{"key":"rf7","volume-title":"A First Course in Fuzzy Logic","author":"Nguyen H.","year":"2000"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.2307\/1969678"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/s00010-002-8005-9"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-006-0127-x"},{"key":"rf11","doi-asserted-by":"crossref","first-page":"41","DOI":"10.33232\/BIMS.0054.41.52","volume":"54","author":"O'Farrell A.","journal-title":"Bulletin of the Irish Mathematical Society"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2005.01.011"},{"key":"rf13","first-page":"79","volume":"5","author":"Burgu\u00e9s C.","journal-title":"Stochastica"},{"key":"rf14","doi-asserted-by":"crossref","first-page":"99","DOI":"10.36045\/bbms\/1172852247","volume":"14","author":"Maes K. C.","journal-title":"Bulletin of the Belgian Mathematical Society \u2014 Simon Stevin"}],"container-title":["International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218488509005826","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,24]],"date-time":"2023-05-24T17:07:58Z","timestamp":1684948078000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218488509005826"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,4]]},"references-count":13,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2009,4]]}},"alternative-id":["10.1142\/S0218488509005826"],"URL":"https:\/\/doi.org\/10.1142\/s0218488509005826","relation":{},"ISSN":["0218-4885","1793-6411"],"issn-type":[{"value":"0218-4885","type":"print"},{"value":"1793-6411","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,4]]}}}