{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T16:43:32Z","timestamp":1783183412771,"version":"3.54.6"},"reference-count":22,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,3,26]],"date-time":"2023-03-26T00:00:00Z","timestamp":1679788800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Spanish Ministry of Science, Innovation, and Universities (MCIU)","award":["FPU19\/01467"],"award-info":[{"award-number":["FPU19\/01467"]}]},{"name":"Spanish Ministry of Science, Innovation, and Universities (MCIU)","award":["PID2021-127870OB-I00"],"award-info":[{"award-number":["PID2021-127870OB-I00"]}]},{"name":"State Agency of Resaearch (AEI)","award":["FPU19\/01467"],"award-info":[{"award-number":["FPU19\/01467"]}]},{"name":"State Agency of Resaearch (AEI)","award":["PID2021-127870OB-I00"],"award-info":[{"award-number":["PID2021-127870OB-I00"]}]},{"name":"European Social Fund (FEDER)","award":["FPU19\/01467"],"award-info":[{"award-number":["FPU19\/01467"]}]},{"name":"European Social Fund (FEDER)","award":["PID2021-127870OB-I00"],"award-info":[{"award-number":["PID2021-127870OB-I00"]}]},{"name":"Spanish Ministry of Science, Innovation, and Universities (MCIU)","award":["FPU19\/01467"],"award-info":[{"award-number":["FPU19\/01467"]}]},{"name":"Spanish Ministry of Science, Innovation, and Universities (MCIU)","award":["PID2021-127870OB-I00"],"award-info":[{"award-number":["PID2021-127870OB-I00"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Preconcepts are basic units of knowledge that form the basis of formal concepts in formal concept analysis (FCA). This paper investigates the relations among different kinds of preconcepts, such as protoconcepts, meet and join-semiconcepts and formal concepts. The first contribution of this paper, is to present a fuzzy powerset lattice gradation, that coincides with the preconcept lattice at its 1-cut. The second and more significant contribution, is to introduce a preconcept algebra gradation that yields different algebras for protoconcepts, semiconcepts, and concepts at different cuts. This result reveals new insights into the structure and properties of the different categories of preconcepts.<\/jats:p>","DOI":"10.3390\/axioms12040324","type":"journal-article","created":{"date-parts":[[2023,3,27]],"date-time":"2023-03-27T03:01:14Z","timestamp":1679886074000},"page":"324","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Fuzzy Algebras of Concepts"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4785-6802","authenticated-orcid":false,"given":"Manuel","family":"Ojeda-Hern\u00e1ndez","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada, Universidad de M\u00e1laga, Andaluc\u00eda Tech, 29071 M\u00e1laga, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0172-1585","authenticated-orcid":false,"given":"Domingo","family":"L\u00f3pez-Rodr\u00edguez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada, Universidad de M\u00e1laga, Andaluc\u00eda Tech, 29071 M\u00e1laga, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5506-6467","authenticated-orcid":false,"given":"Pablo","family":"Cordero","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada, Universidad de M\u00e1laga, Andaluc\u00eda Tech, 29071 M\u00e1laga, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1007\/978-94-009-7798-3_15","article-title":"Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts","volume":"83","author":"Wille","year":"1982","journal-title":"Ordered Sets"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Ganter, B., and Wille, R. 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