Fan Min

Youxi Wu, Shuhui Cheng, Yan Li et al.

The three-way decisions strategy has been employed to construct network topology in a single hidden layer feedforward neural network (SFNN). However, this model has a general performance, and does not consider the process costs, since it has fixed threshold parameters. Inspired by the sequential three-way decisions (STWD), this paper proposes STWD with an SFNN (STWD-SFNN) to enhance the performance of networks on structured datasets. STWD-SFNN adopts multi-granularity levels to dynamically learn the number of hidden layer nodes from coarse to fine, and set the sequential threshold parameters. Specifically, at the coarse granular level, STWD-SFNN handles easy-to-classify instances by applying strict threshold conditions, and with the increasing number of hidden layer nodes at the fine granular level, STWD-SFNN focuses more on disposing of the difficult-to-classify instances by applying loose threshold conditions, thereby realizing the classification of instances. Moreover, STWD-SFNN considers and reports the process cost produced from each granular level. The experimental results verify that STWD-SFNN has a more compact network on structured datasets than other SFNN models, and has better generalization performance than the competitive models. All models and datasets can be downloaded from https://github.com/wuc567/Machine-learning/tree/main/STWD-SFNN.

Qiyang Yu, Yu Fang, Tianrui Li et al.

Prompt-free image segmentation aims to generate accurate masks without manual guidance. Typical pre-trained models, notably Segmentation Anything Model (SAM), generate prompts directly at a single granularity level. However, this approach has two limitations: (1) Localizability, lacking mechanisms for autonomous region localization; (2) Scalability, limited fine-grained modeling at high resolution. To address these challenges, we introduce Granular Computing-driven SAM (Grc-SAM), a coarse-to-fine framework motivated by Granular Computing (GrC). First, the coarse stage adaptively extracts high-response regions from features to achieve precise foreground localization and reduce reliance on external prompts. Second, the fine stage applies finer patch partitioning with sparse local swin-style attention to enhance detail modeling and enable high-resolution segmentation. Third, refined masks are encoded as latent prompt embeddings for the SAM decoder, replacing handcrafted prompts with an automated reasoning process. By integrating multi-granularity attention, Grc-SAM bridges granular computing with vision transformers. Extensive experimental results demonstrate Grc-SAM outperforms baseline methods in both accuracy and scalability. It offers a unique granular computational perspective for prompt-free segmentation.

Qiyang Yu, Yu Fang, Tianrui Li et al.

Vision Transformers (ViTs) have demonstrated strong capabilities in capturing global dependencies but often struggle to efficiently represent fine-grained local details. Existing multi-scale approaches alleviate this issue by integrating hierarchical or hybrid features; however, they rely on fixed patch sizes and introduce redundant computation. To address these limitations, we propose Granularity-driven Vision Transformer (Grc-ViT), a dynamic coarse-to-fine framework that adaptively adjusts visual granularity based on image complexity. It comprises two key stages: (1) Coarse Granularity Evaluation module, which assesses visual complexity using edge density, entropy, and frequency-domain cues to estimate suitable patch and window sizes; (2) Fine-grained Refinement module, which refines attention computation according to the selected granularity, enabling efficient and precise feature learning. Two learnable parameters, α and \b{eta}, are optimized end-to-end to balance global reasoning and local perception. Comprehensive evaluations demonstrate that Grc-ViT enhances fine-grained discrimination while achieving a superior trade-off between accuracy and computational efficiency.

Fan Min, William Zhu

Recommender systems are important for e-commerce companies as well as researchers. Recently, granular association rules have been proposed for cold-start recommendation. However, existing approaches reserve only globally strong rules; therefore some users may receive no recommendation at all. In this paper, we propose to mine the top-k granular association rules for each user. First we define three measures of granular association rules. These are the source coverage which measures the user granule size, the target coverage which measures the item granule size, and the confidence which measures the strength of the association. With the confidence measure, rules can be ranked according to their strength. Then we propose algorithms for training the recommender and suggesting items to each user. Experimental are undertaken on a publicly available data set MovieLens. Results indicate that the appropriate setting of granule can avoid over-fitting and at the same time, help obtaining high recommending accuracy.

Fan Min, William Zhu

Recommender systems are popular in e-commerce as they suggest items of interest to users. Researchers have addressed the cold-start problem where either the user or the item is new. However, the situation with both new user and new item has seldom been considered. In this paper, we propose a cold-start recommendation approach to this situation based on granular association rules. Specifically, we provide a means for describing users and items through information granules, a means for generating association rules between users and items, and a means for recommending items to users using these rules. Experiments are undertaken on a publicly available dataset MovieLens. Results indicate that rule sets perform similarly on the training and the testing sets, and the appropriate setting of granule is essential to the application of granular association rules.

Fan Min, William Zhu

Granular association rule is a new approach to reveal patterns hide in many-to-many relationships of relational databases. Different types of data such as nominal, numeric and multi-valued ones should be dealt with in the process of rule mining. In this paper, we study multi-valued data and develop techniques to filter out strong however uninteresting rules. An example of such rule might be "male students rate movies released in 1990s that are NOT thriller." This kind of rules, called negative granular association rules, often overwhelms positive ones which are more useful. To address this issue, we filter out negative granules such as "NOT thriller" in the process of granule generation. In this way, only positive granular association rules are generated and strong ones are mined. Experimental results on the movielens data set indicate that most rules are negative, and our technique is effective to filter them out.

Hong Zhao, Fan Min, William Zhu

The measurement error with normal distribution is universal in applications. Generally, smaller measurement error requires better instrument and higher test cost. In decision making based on attribute values of objects, we shall select an attribute subset with appropriate measurement error to minimize the total test cost. Recently, error-range-based covering rough set with uniform distribution error was proposed to investigate this issue. However, the measurement errors satisfy normal distribution instead of uniform distribution which is rather simple for most applications. In this paper, we introduce normal distribution measurement errors to covering-based rough set model, and deal with test-cost-sensitive attribute reduction problem in this new model. The major contributions of this paper are four-fold. First, we build a new data model based on normal distribution measurement errors. With the new data model, the error range is an ellipse in a two-dimension space. Second, the covering-based rough set with normal distribution measurement errors is constructed through the "3-sigma" rule. Third, the test-cost-sensitive attribute reduction problem is redefined on this covering-based rough set. Fourth, a heuristic algorithm is proposed to deal with this problem. The algorithm is tested on ten UCI (University of California - Irvine) datasets. The experimental results show that the algorithm is more effective and efficient than the existing one. This study is a step toward realistic applications of cost-sensitive learning.

Fan Min, William Zhu

Granular association rules reveal patterns hide in many-to-many relationships which are common in relational databases. In recommender systems, these rules are appropriate for cold start recommendation, where a customer or a product has just entered the system. An example of such rules might be "40% men like at least 30% kinds of alcohol; 45% customers are men and 6% products are alcohol." Mining such rules is a challenging problem due to pattern explosion. In this paper, we propose a new type of parametric rough sets on two universes to study this problem. The model is deliberately defined such that the parameter corresponds to one threshold of rules. With the lower approximation operator in the new parametric rough sets, a backward algorithm is designed for the rule mining problem. Experiments on two real world data sets show that the new algorithm is significantly faster than the existing sandwich algorithm. This study indicates a new application area, namely recommender systems, of relational data mining, granular computing and rough sets.

Fan Min, Qinghua Hu, William Zhu

Feature selection is an important preprocessing step in machine learning and data mining. In real-world applications, costs, including money, time and other resources, are required to acquire the features. In some cases, there is a test cost constraint due to limited resources. We shall deliberately select an informative and cheap feature subset for classification. This paper proposes the feature selection with test cost constraint problem for this issue. The new problem has a simple form while described as a constraint satisfaction problem (CSP). Backtracking is a general algorithm for CSP, and it is efficient in solving the new problem on medium-sized data. As the backtracking algorithm is not scalable to large datasets, a heuristic algorithm is also developed. Experimental results show that the heuristic algorithm can find the optimal solution in most cases. We also redefine some existing feature selection problems in rough sets, especially in decision-theoretic rough sets, from the viewpoint of CSP. These new definitions provide insight to some new research directions.

Shiping Wang, Qingxin Zhu, William Zhu et al.

Covering is an important type of data structure while covering-based rough sets provide an efficient and systematic theory to deal with covering data. In this paper, we use boolean matrices to represent and axiomatize three types of covering approximation operators. First, we define two types of characteristic matrices of a covering which are essentially square boolean ones, and their properties are studied. Through the characteristic matrices, three important types of covering approximation operators are concisely equivalently represented. Second, matrix representations of covering approximation operators are used in boolean matrix decomposition. We provide a sufficient and necessary condition for a square boolean matrix to decompose into the boolean product of another one and its transpose. And we develop an algorithm for this boolean matrix decomposition. Finally, based on the above results, these three types of covering approximation operators are axiomatized using boolean matrices. In a word, this work borrows extensively from boolean matrices and present a new view to study covering-based rough sets.