{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:29:09Z","timestamp":1777703349643,"version":"3.51.4"},"reference-count":4,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2015,10,23]],"date-time":"2015-10-23T00:00:00Z","timestamp":1445558400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2015,10,23]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>To take into account that expert\u2019s degrees of certainty are not always comparable, researchers have used partially ordered set of degrees instead of the more traditional linearly (totally) ordered interval [0, 1]. In most cases, it is assumed that this partially ordered set is a lattice, i.e., every two elements have the greatest lower bound and the least upper bound. In this paper, we prove a theorem explaining why it is reasonable to require that the set of degrees is a lattice.<\/jats:p>","DOI":"10.3233\/ifs-151558","type":"journal-article","created":{"date-parts":[[2015,11,3]],"date-time":"2015-11-03T11:20:46Z","timestamp":1446549646000},"page":"1421-1425","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Why Lattice-valued fuzzy values? A\u00a0mathematical justification"],"prefix":"10.1177","volume":"29","author":[{"given":"Rujira","family":"Ouncharoen","sequence":"first","affiliation":[{"name":"Department of Mathematics, Chiang Mai University, Chiang Mai, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vladik","family":"Kreinovich","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Texas at El Paso, 500 W. University, El Paso, TX, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hung T.","family":"Nguyen","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, USA"},{"name":"Faculty of Economics, Chiang Mai University, Chiang Mai, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2015,10,23]]},"reference":[{"key":"e_1_3_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(67)90189-8"},{"key":"e_1_3_1_3_1","unstructured":"KlirGYuanB1995Fuzzy Sets and Fuzzy LogicPrentice HallUpper Saddle River New Jersey"},{"key":"e_1_3_1_4_1","unstructured":"NguyenHTWalkerEA2006A First Course in Fuzzy LogicChapman and Hall\/CRCBoca Raton Florida"},{"key":"e_1_3_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/IFS-151558","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/IFS-151558","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/IFS-151558","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:38:30Z","timestamp":1777455510000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/IFS-151558"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10,23]]},"references-count":4,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2015,10,23]]}},"alternative-id":["10.3233\/IFS-151558"],"URL":"https:\/\/doi.org\/10.3233\/ifs-151558","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,10,23]]}}}