JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

Based on multi-scale feature fusion and improved attention for rusty bolt and nut detection

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2026, 61(1): 1-14. doi:10.6040/j.issn.1671-9352.5.2025.067

Abstract ( 64 )

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To address the detection challenges associated with bolts and nuts in transmission line inspections—such as small object sizes, large quantities, and complex background occlusions,the method of bolt-nut detection Transformer(BN-DETR)incorporating a multi-scale feature fusion mechanism and enhanced attention mechanisms is proposed. A feature extraction module is constructed utilizing the cross-stage partial darknet(CSPDarknet)as the backbone, which efficiently aggregates multi-scale features through the integration of local perception, global attention mechanisms, and multi-layer perceptron. Scale-wise feature interaction module based on improved attention is designed to dynamically select key sampling points, thereby reducing computational complexity while preserving global information exchange. A multi-level attention fusion mechanism encompassing global, local, and pixel-level attention are introduced to augment feature representation. Experimental results demonstrate that, on a self-constructed dataset of corroded bolts in transmission lines, BN-DETR achieves 3% improvement in the @50 metric relative to the baseline algorithm. The proposed method offers an effective technical reference for the detection of small defects in power infrastructure.

Lightweight water surface small object detection model with multi-scale attention mechanism and improved feature fusion

ZHONG Shang, MA Li, LIU Wenzhe, LI Yuhao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2026, 61(1): 15-25. doi:10.6040/j.issn.1671-9352.8.2024.013

Abstract ( 65 )

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In complex water surface scenarios, addressing the issues of low detection accuracy, high missed detection rates, and limited computational resources for small target detection, this paper proposes a lightweight water surface small object detection model with multi-scale attention mechanism and improved feature fusion. Based on centerness theory, a new backbone network is designed, leveraging the multi-scale attention mechanism to enhance the models feature extraction capabilities. Partial convolution is used to improve the neck network by reducing feature map redundancy, effectively lowering the models computational load. A large separable kernel attention module is employed to improve the spatial pyramid pooling module, enhancing the models feature fusion ability. Experimental results demonstrate that, compared to other models, the proposed model achieves higher detection accuracy, lower missed detection rates, and fewer parameters.

Analysis of the prediction model based on deep neural networks for mortality risk prediction for sepsis patients in intensive care units

YU Lei, SUN Yi, HUA Jinming, LI Laquan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2026, 61(1): 26-35. doi:10.6040/j.issn.1671-9352.8.2024.009

Abstract ( 44 )

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A deep neural network(DNN)model is proposed by integrating variable selection networks(VSN)and gated residual networks(GRN)to predict the 30-day mortality risk of sepsis patients in the intensive care unit(ICU)and to conduct an in-depth interpretability analysis. In the critical care medical database, 43 significant features are selected using a random forest algorithm, and the proposed model is employed to evaluate mortality risk. The remove and retrain(ROAR)method is utilized to determine the optimal interpretability approach for explaining the results. Testing outcomes indicate that the proposed model outperforms other machine learning models, achieving an area under the receiver operating characteristic curve(AUROC)of 0.967. In the ROAR analysis, the AUROC of the layer-wise relevance propagation(LRP)method decreases from 0.967 to 0.828. Through interpretability analysis of the proposed model using LRP, the Charlson comorbidity score is identified as the most critical feature. In contrast, the organ failure score, age, and respiratory rate also have a pronounced impact on the mortality risk of ICU sepsis patients.

Fuzzy mathematical morphology edge detection method derived from general overlap functions

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2026, 61(1): 36-48. doi:10.6040/j.issn.1671-9352.0.2025.088

Abstract ( 40 )

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Two types of fuzzy mathematical morphology operators are constructed based on the general overlap function, and the corresponding fuzzy mathematical morphological edge detection methods are proposed, which are successfully applied to image edge extraction. Based on the general overlap functions and their corresponding residuated implications, two types of fuzzy mathematical morphological operators, including fuzzy erosion and fuzzy dilation, are constructed, respectively, and their related algebraic properties are studied. A new fuzzy mathematical morphological edge detection method is proposed by combining the fuzzy clustering method with the fuzzy erosion and fuzzy dilation. This edge detection method is wider than that of the edge detection method of the triangular norms and the classical conjuction, and the experimental results show that the noise introduction rate can be effectively reduced under the premise of extracting the edge of the complete image as much as possible.

Fuzzy rough c-means based on the knowledge measure

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2026, 61(1): 49-64. doi:10.6040/j.issn.1671-9352.4.2025.004

Abstract ( 33 )

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A knowledge-based fuzzy rough c-means clustering method(KFRCM)is introduced. Traditional clustering methods have limitations in handling data with fuzzy boundaries, which are sensitive to the initial cluster centers, and exhibit low efficiency in high-dimensional spaces. To address these issues, the KFRCM is proposed. a feature-weighted knowledge measure is incorporated, fuzzy membership functions are integrated with rough set approximation operators, and Gaussian kernel similarity is utilized to enhance boundary characterization. Experimental results on 14 datasets demonstrate that the proposed KFRCM algorithm outperforms 6 mainstream clustering algorithms in terms of accuracy, stability, and computational efficiency. This study is recognized as the first integration of knowledge measurement with fuzzy rough clustering, offering a new perspective and an advanced algorithmic framework for developing more reliable and adaptable clustering techniques.

Three-way K-means algorithm combining the bat algorithm and the improved compactness

SUN Qing, YE Jun, ZENG Guangcai, SONG Suyang, WANG Yixin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2026, 61(1): 65-75. doi:10.6040/j.issn.1671-9352.0.2024.353

Abstract ( 51 )

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The three way K-means algorithm is improved by integrating the bat algorithm with closeness degree optimization. The bat algorithm is optimized by employing the golden section coefficient and population average position. The optimized bat algorithm searches for initial cluster centers which improving the stability of the three way K-means algorithm. Additionally, the threshold for core and boundary regions is determined based on closeness degree, which reduces the number of boundary samples and enhances the accuracy of the three way K-means algorithm. Comparative experiments is conducted on nine datasets against six clustering algorithms. It is shown that the proposed method improves clustering performance and is confirming its effectiveness and practical utility.

Precise morphological recognition with zonal micro-direction for termites

ZOU Zheng, LEI Yusheng, LIU Shijian, WANG Dingyi, QIU Xuewei, SHI Wenwen, ZHOU Xiaotong

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2026, 61(1): 76-84. doi:10.6040/j.issn.1671-9352.5.2025.118

Abstract ( 29 )

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The partition-based approach is used in the paper to refine the target by indirectly enhancing the salience of morphological differences. Rotational moment-based representation is provided more directional information, and a multi-layer local spatial perception module is incorporated to directly associate direction with features. Furthermore, a dual-branch spatial pyramid module is introduced to enhance the reuse of shallow features and improve computational efficiency. In our experiments, the rotational object detection method, the key point detection method, and the proposed method are compared, and it is demonstrated that our method achieves better accuracy and robustness in extracting the direction and position of small targets under higher interference.

Fuzzy rough set model based on type-2 fuzzy preorders

ZHANG Guangxu, YAO Wei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2026, 61(1): 85-93. doi:10.6040/j.issn.1671-9352.0.2024.035

Abstract ( 34 )

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Based on the fundamental structure of type-2 fuzzy preorders, fuzzy rough sets are investigated, and a pair of fuzzy upper and lower approximation operators are defined. Furthermore, their properties and interrelations are explored. It is shown that upper definable sets and lower definable sets are equivalent. Definable sets form a stratified Alexandrov fuzzy topology such that the upper and lower approximation operators are the related closure and interior operators respectively.

Hybrid mutation based gray wolf optimization algorithm for berth-quay crane scheduling

YANG Yu, SUN Shengbo, XU Zirui, JIANG Xiaowei, SONG Qiang, DAI Hongwei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2026, 61(1): 94-102. doi:10.6040/j.issn.1671-9352.1.2024.752

Abstract ( 38 )

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In order to address the issues of slow convergence speed and susceptibility to local optimality in the gray wolf optimizer(GWO)algorithm, a hybrid mutation gray wolf optimizer(HMGWO)algorithm is proposed. This new algorithm is based on hybrid mutation and utilizes the Tent chaotic mapping strategy. The population is initialized, and an adaptive convergence factor strategy is incorporated to maintain search diversity. Additionally, the algorithm introduces the Gaussian-Cauchy hybrid mutation strategy to enhance performance. Six benchmark test functions are utilized for simulation experiments, evaluating the HMGWO algorithms optimization capability and convergence. The HMGWO algorithm was applied to the discrete berth-quay crane scheduling problem. After one thousand iterations in experiments, the HMGWO algorithm spent the shortest time for ships in port.

Gray-vlsekriterijumska optimizacija i kompromisno resenje method based on subtraction and division operators in T-spherical fuzzy environment

DENG Shihai, ZHENG Tingting, LAI Longxiang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2026, 61(1): 103-115. doi:10.6040/j.issn.1671-9352.0.2024.429

Abstract ( 32 )

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The subtraction and division operators for T-spherical fuzzy numbers are proposed, and the properties of these subtraction and division operators for T-spherical fuzzy numbers are discussed. A grey relational analysis method based on T-spherical fuzzy subtraction and division operators is introduced. This method is then integrated with the vlsekriterijumska optimizacija i kompromisno resenje(VIKOR)method to prevent the loss of T-spherical fuzzy information during calculations. Additionally, a novel score function is employed to refine the comparison mechanism for T-spherical fuzzy numbers. The validity and superiority of the proposed grey-VIKOR method, grounded in T-spherical fuzzy subtraction and division operators, are demonstrated through illustrative examples and comparative experiments. This approach provides a novel and effective methodology for addressing multi-attribute decision-making problems in T-spherical fuzzy environments.

Type-2 hesitant q-rung triangular uncertain linguistic Schweizer-Sklar-Muirhead operators

LÜ Xiaofan, YUAN Xiujiu, LI Jingtai, ZHAO Xuejun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2026, 61(1): 116-126. doi:10.6040/j.issn.1671-9352.0.2024.108

Abstract ( 33 )

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In order to describe the multi-layer hesitation of decision-makers in multi-attribute decision-making problems, the type-2 hesitant q-rung triangular uncertain linguistic set is defined by combining hesitant fuzzy set, q-rung triangular hesitant fuzzy set and q-rung hesitant fuzzy uncertain linguistic set. Based on the Schweizer-Sklar norm, the operation laws and properties of the type-2 hesitant q-rung triangular uncertain linguistic fuzzy elements are discussed. In addition, in order to better handle the practical problem with interrelated evaluation attributes, the Muirhead mean operator is extended to the type-2 hesitant q-rung triangular uncertain linguistic set, and the type-2 hesitant q-rung triangular uncertain linguistic Schweizer-Sklar-Muirhead mean operator and its weighted form are proposed. Moreover, the calculation formulae of the operators are given and their properties are discussed. Finally, a multi-attribute decision-making problem model based on the type-2 q-rung hesitant triangular fuzzy uncertain linguistic weighted Muirhead mean operator is established and further analyzed by a numerical example.

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