{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:25:28Z","timestamp":1760145928246,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,16]],"date-time":"2024-09-16T00:00:00Z","timestamp":1726444800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Scientific Research Project of Mudanjiang Normal University","award":["MNUGP202303","12271036","11871097","1355JG010"],"award-info":[{"award-number":["MNUGP202303","12271036","11871097","1355JG010"]}]},{"name":"National Natural Science Foundation of China","award":["MNUGP202303","12271036","11871097","1355JG010"],"award-info":[{"award-number":["MNUGP202303","12271036","11871097","1355JG010"]}]},{"name":"Heilongjiang Provincial Department of Education research record key project","award":["MNUGP202303","12271036","11871097","1355JG010"],"award-info":[{"award-number":["MNUGP202303","12271036","11871097","1355JG010"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The aim of this paper is to examine the L-fuzzy prime filter degrees on lattices and their induced L-fuzzy convex structure. Firstly, the notion of L-fuzzy prime filter degrees on lattices is established using the implication operator when L is a completely distributive lattice. Secondly, an equivalent characterization of L-fuzzy prime filter degrees on lattices is provided. The equivalence relation, through the definitions of reflexivity, symmetry, and transitivity, provides a method for partitioning subsets within a lattice that possesses the prime filter property. Finally, the L-fuzzy convex structure induced by the L-fuzzy prime filter degrees on lattices is examined. Simultaneously, the properties of L-fuzzy prime filter degrees on lattices in relation to images and preimages under homomorphic mappings are discussed.<\/jats:p>","DOI":"10.3390\/sym16091215","type":"journal-article","created":{"date-parts":[[2024,9,16]],"date-time":"2024-09-16T04:14:07Z","timestamp":1726460047000},"page":"1215","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The L-Fuzzy Prime Filter Degrees on Lattices and Its Induced L-Fuzzy Convex Structure"],"prefix":"10.3390","volume":"16","author":[{"given":"Lan","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Mudanjiang Normal University, Mudanjiang 157011, China"}]},{"given":"Jing","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Mudanjiang Normal University, Mudanjiang 157011, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,16]]},"reference":[{"key":"ref_1","unstructured":"Zhang, X.H. 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