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Keywords = axiomatic fuzzy set (AFS)

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17 pages, 15672 KB  
Article
Optimizing Parameters of Marine Hydrodynamic Models Based on AFS Theory and PCA
by Yangxin Zhang, Jiangmei Zhang, Xinghua Feng, Haolin Liu, Guowei Yang, Tuantuan Liu, Yongzhuo Liu and Jiaze Li
Water 2025, 17(21), 3089; https://doi.org/10.3390/w17213089 - 28 Oct 2025
Viewed by 756
Abstract
The parameter optimization of marine hydrodynamic models currently relies predominantly on expert empirical knowledge, but the quantitative indicators and weighting mechanisms for rapid calibration remain unclear due to inherent model uncertainties and complexities. This study addresses these challenges through expert questionnaires that collect [...] Read more.
The parameter optimization of marine hydrodynamic models currently relies predominantly on expert empirical knowledge, but the quantitative indicators and weighting mechanisms for rapid calibration remain unclear due to inherent model uncertainties and complexities. This study addresses these challenges through expert questionnaires that collect fuzzy evaluations of calibration criteria, developing an integrated methodology combining the theory of axiomatic fuzzy set (AFS) with principal component analysis (PCA). Numerical case studies quantify calibration indicator weights and assess critical parameter impacts, revealing that bathymetry and roughness coefficients predominantly govern simulation accuracy. Elevated roughness conditions demonstrate two regimes: (1) at 1–2 × baseline roughness, strong positive correlations (with a coefficient of determination R2 increased by up to 0.568 compared to baseline) confirm effective model-data matching for tidal levels/currents; (2) beyond 2 × baseline roughness, progressive correlation decay accompanies increasing coefficients, indicating amplified simulation–measurement discrepancies. Notably, under reduced roughness conditions, high accuracy persists during spring/mid-tide phases but significantly diminishes during neap tides, demonstrating enhanced roughness sensitivity in low-tidal energy regimes. Full article
(This article belongs to the Section Oceans and Coastal Zones)
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11 pages, 701 KB  
Article
A Novel Fuzzy Bi-Clustering Algorithm with Axiomatic Fuzzy Set for Identification of Co-Regulated Genes
by Kaijie Xu and Yixi Wang
Mathematics 2024, 12(11), 1659; https://doi.org/10.3390/math12111659 - 26 May 2024
Cited by 4 | Viewed by 1540
Abstract
The identification of co-regulated genes and their Transcription-Factor Binding Sites (TFBSs) are the key steps toward understanding transcription regulation. In addition to effective laboratory assays, various bi-clustering algorithms for the detection of the co-expressed genes have been developed. Bi-clustering methods are used to [...] Read more.
The identification of co-regulated genes and their Transcription-Factor Binding Sites (TFBSs) are the key steps toward understanding transcription regulation. In addition to effective laboratory assays, various bi-clustering algorithms for the detection of the co-expressed genes have been developed. Bi-clustering methods are used to discover subgroups of genes with similar expression patterns under to-be-identified subsets of experimental conditions when applied to gene expression data. By building two fuzzy partition matrices of the gene expression data with the Axiomatic Fuzzy Set (AFS) theory, this paper proposes a novel fuzzy bi-clustering algorithm for the identification of co-regulated genes. Specifically, the gene expression data are transformed into two fuzzy partition matrices via the sub-preference relations theory of AFS at first. One of the matrices considers the genes as the universe and the conditions as the concept, and the other one considers the genes as the concept and the conditions as the universe. The identification of the co-regulated genes (bi-clusters) is carried out on the two partition matrices at the same time. Then, a novel fuzzy-based similarity criterion is defined based on the partition matrices, and a cyclic optimization algorithm is designed to discover the significant bi-clusters at the expression level. The above procedures guarantee that the generated bi-clusters have more significant expression values than those extracted by the traditional bi-clustering methods. Finally, the performance of the proposed method is evaluated with the performance of the three well-known bi-clustering algorithms on publicly available real microarray datasets. The experimental results are in agreement with the theoretical analysis and show that the proposed algorithm can effectively detect the co-regulated genes without any prior knowledge of the gene expression data. Full article
(This article belongs to the Special Issue New Advances in Data Analytics and Mining)
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