{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T04:54:07Z","timestamp":1768452847646,"version":"3.49.0"},"reference-count":42,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,3,22]],"date-time":"2021-03-22T00:00:00Z","timestamp":1616371200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Noticing certain limitations of concept lattices in the fuzzy context, especially in view of their practical applications, in this paper, we propose a more general approach based on what we call graded fuzzy preconcept lattices. We believe that this approach is more adequate for dealing with fuzzy information then the one based on fuzzy concept lattices. We consider two possible gradation methods of fuzzy preconcept lattice\u2014an inner one, called D-gradation and an outer one, called M-gradation, study their properties, and illustrate by a series of examples, in particular, of practical nature.<\/jats:p>","DOI":"10.3390\/axioms10010041","type":"journal-article","created":{"date-parts":[[2021,3,22]],"date-time":"2021-03-22T11:13:26Z","timestamp":1616411606000},"page":"41","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Gradation of Fuzzy Preconcept Lattices"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3763-7032","authenticated-orcid":false,"given":"Alexander","family":"\u0160ostak","sequence":"first","affiliation":[{"name":"Institute of Mathematics and CS University of Latvia, LV-1459 Riga, Latvia"},{"name":"Department of Mathematics, University of Latvia, LV-1004 Riga, Latvia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ingr\u012bda","family":"U\u013cjane","sequence":"additional","affiliation":[{"name":"Institute of Mathematics and CS University of Latvia, LV-1459 Riga, Latvia"},{"name":"Department of Mathematics, University of Latvia, LV-1004 Riga, Latvia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M\u0101ris","family":"Krasti\u0146\u0161","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Latvia, LV-1004 Riga, Latvia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1016\/0898-1221(92)90120-7","article-title":"Concept lattices and conceptual knowledge systems","volume":"23","author":"Wille","year":"1992","journal-title":"Comp. 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