{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:20:45Z","timestamp":1760170845922},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[2014,4]]},"abstract":"<jats:p> The well-known Boolean-law \u201c\u03b1 \u2192 (\u03b2 \u2192 \u03b1) = 1\u201d can be generalized to fuzzy context as I(x, I(y, x)) = 1, where I is a fuzzy implication. In this paper we show the necessary and sufficient conditions under which this generalization holds in fuzzy logics. We focus the investigation on the following classes of fuzzy implication: (S,N)-, R-, QL-, D- and (N, T)-implications. In addition, we demonstrate that a fuzzy implication I satisfies such Boolean-like law if, and only if, its \u0424-conjugate also satisfies it. <\/jats:p>","DOI":"10.1142\/s0218488514500093","type":"journal-article","created":{"date-parts":[[2014,4,14]],"date-time":"2014-04-14T08:19:50Z","timestamp":1397463590000},"page":"205-215","source":"Crossref","is-referenced-by-count":8,"title":["On the Boolean-like Law I(x, I(y, x)) = 1"],"prefix":"10.1142","volume":"22","author":[{"given":"Anderson","family":"Cruz","sequence":"first","affiliation":[{"name":"Metr\u00f3pole Digital Institute, Federal University of Rio Grande do Norte \u2013 UFRN, Natal, Rio Grande do Norte, 59072-970, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Benjam\u00edn","family":"Bedregal","sequence":"additional","affiliation":[{"name":"Group for Logic, Language, Information, Theory and Applications \u2013 LoLITA, Department of Informatics and Applied Mathematics \u2013 DIMAp, Federal University of Rio Grande do Norte \u2013 UFRN, Natal, Rio Grande do Norte, 59072-970, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Regivan","family":"Santiago","sequence":"additional","affiliation":[{"name":"Group for Logic, Language, Information, Theory and Applications \u2013 LoLITA, Department of Informatics and Applied Mathematics \u2013 DIMAp, Federal University of Rio Grande do Norte \u2013 UFRN, Natal, Rio Grande do Norte, 59072-970, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2014,4,14]]},"reference":[{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1109\/91.983281"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2004.825075"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2007.01.026"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2007.895969"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1093\/jigpal\/jzn012"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-005-0526-4"},{"key":"p_10","first-page":"491","volume":"159","author":"Sainio E.","year":"2008","journal-title":"Systems"},{"key":"p_11","first-page":"209","volume":"134","author":"Bustince H.","year":"2003","journal-title":"Systems"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2007.896304"},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1002\/int.20068"},{"key":"p_14","first-page":"315","volume":"42","author":"Mas M.","year":"2006","journal-title":"Kybernetika"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgor.2007.04.003"}],"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\/S0218488514500093","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T16:47:48Z","timestamp":1565110068000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218488514500093"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,4]]},"references-count":12,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2014,4,14]]},"published-print":{"date-parts":[[2014,4]]}},"alternative-id":["10.1142\/S0218488514500093"],"URL":"https:\/\/doi.org\/10.1142\/s0218488514500093","relation":{},"ISSN":["0218-4885","1793-6411"],"issn-type":[{"value":"0218-4885","type":"print"},{"value":"1793-6411","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,4]]}}}