{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:01:31Z","timestamp":1760148091992,"version":"build-2065373602"},"reference-count":59,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,3,27]],"date-time":"2023-03-27T00:00:00Z","timestamp":1679875200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of P.R. China","doi-asserted-by":"publisher","award":["62176142","LJ2020007"],"award-info":[{"award-number":["62176142","LJ2020007"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Foundation of Liaoning Educational Committee","award":["62176142","LJ2020007"],"award-info":[{"award-number":["62176142","LJ2020007"]}]},{"name":"Special Foundation for Distinguished Professors of Shandong Jianzhu University","award":["62176142","LJ2020007"],"award-info":[{"award-number":["62176142","LJ2020007"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Knowledge reduction is a crucial topic in formal concept analysis. There always exists uncertain, symmetric linguistic-evaluation information in social life, which leads to high complexity in the process of knowledge representation. In order to overcome this problem, we are focused on studying the linguistic-concept-reduction methods in an uncertain environment with fuzzy linguistic information. Based on three-way decisions and an attribute-oriented concept lattice, we construct a fuzzy-object-induced three-way attribute-oriented linguistic (FOEAL) concept lattice, which provides complementary conceptual structures of a three-way concept lattice with symmetric linguistic-evaluation information. Through the granular concept of the FOEAL lattice, we present the corresponding linguistic concept granular consistent set and granular reduction. Then, we further employ the linguistic concept discernibility matrix and discernibility function to calculate the granular reduction set. A similar issue on information entropy is investigated to introduce a method of entropy reduction for the FOEAL lattice, and the relation between the linguistic concept granular reduction and entropy reduction is discussed. The efficiency of the proposed method is depicted by some examples and comparative analysis.<\/jats:p>","DOI":"10.3390\/sym15040813","type":"journal-article","created":{"date-parts":[[2023,3,27]],"date-time":"2023-03-27T06:46:19Z","timestamp":1679899579000},"page":"813","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Linguistic Concept\u2019s Reduction Methods under Symmetric Linguistic-Evaluation Information"],"prefix":"10.3390","volume":"15","author":[{"given":"Hui","family":"Cui","sequence":"first","affiliation":[{"name":"Information Science and Technology College, Dalian Maritime University, Dalian 116026, China"}]},{"given":"Ansheng","family":"Deng","sequence":"additional","affiliation":[{"name":"Information Science and Technology College, Dalian Maritime University, Dalian 116026, China"}]},{"given":"Guanli","family":"Yue","sequence":"additional","affiliation":[{"name":"Information Science and Technology College, Dalian Maritime University, Dalian 116026, China"}]},{"given":"Li","family":"Zou","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Shandong Jianzhu University, Jinan 250101, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4245-8813","authenticated-orcid":false,"given":"Luis","family":"Martinez","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Jaen, 23071 Jaen, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ganter, B., and Wille, R. 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