Breast mass detection remains a significant challenge in developing effective computer-aided diagnosis (CADx) systems to assist clinicians in differentiating between benign and malignant masses. This paper introduces a novel fuzzy rule-based CADx approach for mammographic mass classification, utilising Transformation-based Fuzzy Rule Interpolation with Mahalanobis matrices (MT-FRI). This method enables reliable and interpretable classification by transforming attributes into a new feature space and interpolating for unmatched cases, making it well-suited to limited-data scenarios. The proposed approach integrates a structured pipeline encompassing feature extraction, feature selection, fuzzy rule generation, and interpolation inference, all designed to enhance transparency in diagnostic decisions. The system implementing the approach is evaluated on four widely-used mammographic datasets—INbreast, CBIS-DDSM, BCDR-D01, and BCDR-F01. For the first time, comparative experiments demonstrate that state-of-the-art fuzzy rule interpolative methods, particularly MT-FRI, achieve superior classification performance over representative classical machine learning models and deep neural networks. Unlike deep learning models, which require extensive labelled data and function as ”black boxes”, MT-FRI produces transparent, human-readable rules, supporting clinical interpretability. This work underscores the potential of MT-FRI as an adaptable and interpretable CADx solution for mammographic diagnosis, especially valuable in sparse-data environments.

In recent years, with the rapid development of tourism, the abnormal events in the traffic fortress of tourist attractions not only endanger personal safety, but also cause a lot of negative effects on the society. In the face of the low accuracy of abnormal event detection in complex scenes and the low efficiency of manual observation, combining the advantages and characteristics of YOLOv5 and 3D convolutional neural network(C3D), an automatic abnormal event detection algorithm based on YOLOv5+C3D was proposed. Experimental data show that compared with other methods, the abnormal event detection method based on YOLOv5+C3D has a higher accuracy for various abnormal events detection, indicating that the trained model has a strong generalization ability for abnormal event detection.

In order to solve the problems of low signal-to-noise ratio, uncertain position, and blurred edges of mammography images, and to achieve full-view breast mass segmentation, a breast mass segmentation network based on improved UNet 3+ is proposed. The network provides prior knowledge of edge information for model segmentation by adding an edge-aware module and utilizing shallow and deep features in the network. At the same time, Hybrid loss function (HAM) is added to the network to obtain rich multi-scale information for handling lumps of different sizes and shapes. In addition, we add Dice loss and bce loss to the hybrid loss function to address the problem of pixel class imbalance in mammography images. The experimental results show that the improved UNet 3+ segmentation model has reached the Dice scores of 85.89% and 82.55% on the CBIS-DDSM and INbreast datasets, has improved aa and bb compared with the previous ones, and has a higher performance in the breast mass segmentation task. The accuracy rate is better than other classical models.

A lightweight object detection algorithm based on YOLOv5 is proposed to address the problem of deploying detection models for traffic targets. This method was proposed to reduce the number of channels in the backbone and introduced GSConv to improve performance. At the same time, GSConv was improved to cut the parameters. The C3 module was replaced in the Neck with C2f to obtain more comprehensive gradient flow information. Finally, the model parameters are only 1.41M. Experiment on BDD100K public traffic dataset shows that the lightweight model reduces the number of parameters while losing a small amount of Recalls, and its performance is better than mainstream lightweight networks.

In certain industries such as construction, high risks are often associated with the construction process, and safety helmets are crucial protective gear for workers on construction sites. To address the issues of missed and false detections of safety helmets in complex environments with current helmet detection methods, we propose an improved YOLOv5 object detection algorithm to detect the wearing of safety helmets. The proposed improvements include the addition of an attention mechanism and replacement of the loss function. The proposed method adds an efficient channel attention (ECA) mechanism to the YOLOv5 head network to enhance the model's ability to extract features related to safety helmets, thereby increasing precision without adding too much computational complexity. The loss function is replaced with NWD to effectively improve the detection progress of small safety helmets in YOLOv5.

Abstract Fuzzy rule interpolation (FRI) offers a reliable approach for providing an interpretable approximate decision with a sparse rule base, when a new observation does not match any existing rules. As the mainstream application of a fuzzy rule base is to extract valuable approximate information from each individual rules, existing FRI methods typically work by postulating that the more rules used to implement the interpolation the better the reasoning outcomes. Yet, empirical results have shown that using a large number of rules in an FRI process may adversely lead to worsening the accuracy of the inference outcomes, not just degrading efficiency. The objective of this work is to set a firm theoretical foundation for the eventual establishment of a novel FRI approach. It achieves this goal by mapping the structural patterns within a given fuzzy rule base onto a mathematically isomorphic data space, such that the essential information embedded in the original rule base can be effectively captured, represented and analysed. The resulting mathematically mapped patterns enable the production of a theorem that determines the upper limit of the number of rules required to effectively and efficiently perform FRI. The experimental investigations reported herein demonstrate that the number of required rules to perform FRI obeys the theorem discovered in this work.

Fuzzy rule interpolation (FRI) strongly supports approximate inference when a new observation matches no rules, through selecting and subsequently interpolating appropriate rules close to the observation from the given (sparse) rule base. Traditional ways of implementing the critical rule selection process are typically based on the exploitation of Euclidean distances between the observation and rules. It is conceptually straightforward for implementation but applying this distance metric may systematically lead to inferior results because it fails to reflect the variations of the relevance or significance levels among different domain features. To address this important issue, a novel transformation-based FRI approach is presented, on the basis of utilizing the Mahalanobis distance metric. The new FRI method works by transforming a given sparse rule base into a coordinates system where the distance between instances of the same category becomes closer while that between different categories becomes further apart. In so doing, when an observation is present that matches no rules, the most relevant neighboring rules to implement the required interpolation are more likely to be selected. Following this, the scale and move factors within the classical transformation-based FRI procedure are also modified by Choquet integral. Systematic experimental investigation over a range of classification problems demonstrates that the proposed approach remarkably outperforms the existing state-of-the-art FRI methods in both accuracy and efficiency.

Traditional fuzzy rule interpolation (FRI) methods typically utilise Euclidean distances between an observation and the rules in a given sparse rule base to select a set of rules closest to the observation to perform interpolation. However, simply applying the Euclidean distance metric may frequently lead to inferior results, because it cannot take into consideration the relevance degree of different features. To address this important issue, this paper presents an initial framework for a novel FRI approach which works based on exploiting a transformed rule base. Mahalanobis matrix learned by metric learning methods is used herein to transform the given sparse rule base to a new coordinates system where the distance between instances of the same category is closer, and instances of different categories is distant from each other. When a new observation is present which matches no rules, the selection of the nearest rules to implement the required interpolation is carried out in the transformed coordinates system. Then, the scale and move factors within the classical transformation-based FRI procedure are modified by Choquet integral. Experimental results obtained by employing different metric learning methods and Choquet integral over seven classification problems demonstrate that the proposed approach remarkably outperforms existing FRI methods.

Recently proposed methods of TSK inference extension (TSK+) and K closest rules based TSK (KCR) are able to potentially perform fuzzy rule-based inference with a sparse rule base, for regression problems. However, in certain real-world applications, observations may be rather far away from any rules that may be fired in order to implement the required regression and hence, these state-of-the-art techniques may not work satisfactorily. To investigate an alternative to address such practical problems, this paper presents a novel fuzzy rule interpolation (FRI) approach. It works based on integrating feature selection and feature aggregation to attain a rule-ranking list within the given sparse rule base. The process of acquiring an ordered rule list is accomplished offline, with an ordered rule base ready for use prior to the arrival of any observation online. It boosts the computational efficiency of closest rule selection during the FRI process. Initial experimental results demonstrate that the proposed approach is able to address the problems that TSK+ and KCR fail to do while having a similar time efficiency to them. Further, only two nearest rules to the observation are required to derive interpolated results, thereby significantly improving the automation level of the interpolative reasoning system.

Fuzzy rule-based systems are widely applied for real-world decision support, such as policy formation, public health analysis, medical diagnosis , and risk assessment. However, they face significant challenges when the application problem at hand suffers from the “curse of dimensionality” or “sparse knowledge base” . Combination of hierarchical fuzzy rule models and fuzzy rule interpolation offers a potentially efficient and effective approach to dealing with both of these issues simultaneously. In particular, backward fuzzy rule interpolation (B-FRI) facilitates approximate reasoning to be performed given a sparse rule base where rules do not fully cover all observations or the observations are not complete, missing antecedent values in certain available rules. This paper presents a hierarchical bidirectional fuzzy reasoning mechanism by integrating hierarchical rule structures and forward/backward rule interpolation. A computational method is proposed, building on the resulting hierarchical bidirectional fuzzy interpolation to maintain consistency in sparse fuzzy rule bases. The proposed techniques are utilised to address a range of decision support problems, successfully demonstrating their efficacy.

Intrusion detection system (IDS) is used to find malicious connections and protect networks from external or internal attacks. Various fuzzy or fuzzy intelligence approaches have been proposed in the development of IDS. In particular, the fuzzy interpolation technique guarantees the performance of IDS where only a sparse rule base is available. Furthermore, backward fuzzy interpolation allows interpolation to be carried out when certain antecedents of observation variables are absent, whereas conventional methods do not work. In this paper, a novel fuzzy association rules based classification intrusion detection system framework enhanced by a hierarchical bidirectional fuzzy rule interpolation technique is proposed for designing an IDS. Hierarchical bidirectional fuzzy rule interpolation is also employed to refine fuzzy rule base while which exists some consistency. This framework uses fuzzy association rules for building classifiers, and allows the generation of security alerts from situations which are not directly covered, missing values, or existing inconsistency by knowledge base. The proposed method is herein applied through integration with the Snort software to demonstrate the efficacy of this proposed approach.

Fuzzy rule interpolation is an important technique for performing inference with sparse rule bases. Even when a given observation has no overlap with the antecedent values of any existing rules, fuzzy rule interpolation may still derive a conclusion. In particular, the recently proposed rough-fuzzy rule interpolation offers greater flexibility in handling different levels of uncertainty that may be present in sparse rule bases and observations. Nevertheless, in practical applications with inter-connected subsets of rules, situations may arise where a crucial antecedent of observation is absent, either due to human error or difficulty in obtaining data, while the associated conclusion may be derived according to alternative rules or even observed directly. If such missing antecedents were involved in the subsequent interpolation process, the final conclusion would not be deduced using a forward rule interpolation technique alone. However, missing antecedents may be related to certain intermediate conclusions and therefore, may be interpolated us- ing the known antecedents and these conclusions. Following this idea, a novel backward rough-fuzzy rule interpolation approach is proposed in this paper, allowing missing observations which are indirectly related to the final conclusion to be interpolated from the known antecedents and intermediate conclusions. As illustrated experimentally, the resulting backward rough-fuzzy rule interpolation system is able to deal with uncertainty, in both data and knowledge, with more flexibility.

Fuzzy rule interpolation offers a useful means for enhancing the robustness of fuzzy models by making inference possible in systems of only a sparse rule base. However in practical applications, the rule bases provided may contain irrelevant, redundant, or even misleading antecedents, which makes the already challenging tasks such as inference and interpolation even more difficult. The majority of the techniques developed in the literature assumes equal significance of rules and their antecedents, which may lead to biased or incorrect reasoning outcomes. This paper investigates similar problems being tackled in the area of feature selection, in an attempt to identify techniques that can be applied to measure the significance of rule antecedents. In particular, two feature evaluation methods based on correlation analysis and fuzzy-rough set theory have been examined, in order to reveal their effectiveness in determining the importance of individual antecedents, and their capabilities for discovering subsets of antecedents that provide similar reasoning accuracies as a larger set of antecedents used in the original rules. In addition, the significance values measured by the proposed method are treated as the weights associated with the relevant rule antecedents, in an effort to facilitate more appropriate selection of, and interactions with the rules in performing both forward and backward fuzzy rule interpolation via scale and move transformation-based methods. Experimental studies based on a practical scenario concerning terrorist activities and also synthetic random data are conducted, demonstrating the potential and efficacy of the proposed work.

Fuzzy rule interpolation offers a useful means to enhancing the robustness of fuzzy models by making inference possible in sparse rule-based systems. However, in real-world applications of interconnected rule bases, situations may arise when certain crucial antecedents are absent from given observations. If such missing antecedents were involved in the subsequent interpolation process, the final conclusion would not be deducible using conventional means. To address this important issue, a new approach named backward fuzzy rule interpolation and extrapolation (BFRIE) is proposed in this paper, allowing the observations, which directly relate to the conclusion to be inferred or interpolated from the known antecedents and conclusion. This approach supports both backward interpolation and extrapolation which involve multiple fuzzy rules, with each having multiple antecedents. As such, it significantly extends the existing fuzzy rule interpolation techniques. In particular, considering that there may be more than one antecedent value missing in an application problem, two methods are proposed in an attempt to perform backward interpolation with multiple missing antecedent values. Algorithms are given to implement the approaches via the use of the scale and move transformation-based fuzzy interpolation. Experimental studies that are based on a real-world scenario are provided to demonstrate the potential and efficacy of the proposed work.

Fuzzy rule interpolation offers a useful means for reducing the complexity of fuzzy models, more importantly, it makes inference possible in sparse rule-based systems. Backward fuzzy rule interpolation is a recently proposed technique which extends the potential existing methods, allowing interpolation to be carried out when a certain antecedent of observation is absent. However, only one missing antecedent may be inferred or interpolated using the other given antecedents and the consequent. In this paper, two approaches are proposed in an attempt to perform backward interpolation with multiple missing antecedent values. Both approaches assume a restricted model with multiple inputs and a single output, where every rule has the same number of antecedents. Experimental comparative studies are carried out to demonstrate the efficacy of the proposed work.

Fuzzy rule interpolation is well known for reducing the complexity of fuzzy models and making inference possible in sparse rule-based systems. However, in practical applications with inter-connected subsets of rules, situations may arise when a crucial antecedent of observation is absent, either due to human error or difficulty in obtaining data, while the associated conclusion may be derived according to alternative rules or even observed directly. If such missing antecedents were involved in the subsequent interpolation process, the final conclusion would not be deduced using conventional means. However, missing antecedents may be related to certain conclusion and therefore, may be inferred or interpolated using the known antecedents and conclusion. For this purpose, this paper presents a novel approach termed backward fuzzy rule interpolation and extrapolation. In particular, the approach supports both interpolation and extrapolation which involve multiple intertwined fuzzy rules, with each having multiple antecedents. An algorithm is given to implement the approach via the use of the scale and move transformation-based fuzzy interpolation. The algorithm makes use of trapezoidal fuzzy membership functions. Realistic application examples are provided to demonstrate the efficacy of the approach.