Traditional fuzzy set methods, designed around the finest granularity of inputs-individual points and their membership degrees-often struggle with inefficiencies and label noise. To overcome these challenges, we introduce granular-ball computing into the fuzzy set, creating the new granular-ball fuzzy set framework. This approach uses granular-ball inputs rather than single points, significantly reducing the number of entities and minimizing susceptibility to the noise affecting individual sample points. As a result, our framework enhances both efficiency and robustness compared to traditional methods and is applicable across various domains of fuzzy data processing. Furthermore, we apply this framework to fuzzy support vector machines (FSVMs), developing the Granular-ball Fuzzy Support Vector Machine (GBFSVM). Experimental tests on UCI benchmark datasets show that GBFSVM surpasses traditional models in efficiency and robustness.

Fermatean fuzzy hesitant sets provide a flexible and powerful tool for decision making, allowing decision makers to incorporate uncertainty and hesitation into their decision making process, and enabling them to make more informed and effective decisions in complex and uncertain environments. Considering that many factors are interdependent in reality while existing methods cannot solve this problem, we propose Fermatean hesitant fuzzy Choquet integral ordered aggregation operators based on the Fermatean hesitant fuzzy set and Choquet integral, and establish their related properties. These operators including averaging and geometric operators not only handle situations where decision criteria or preferences are interdependent, but also provides the decision under ideal and non-ideal situation. Additionally, we present a multi-attribute decision-making method for Fermatean hesitant fuzzy information using these operators. We have validated the proposed method, and its practicality and effectiveness are demonstrated through numerical examples from previous research regarding Fermatean Hesitant Fuzzy set, including sensitivity analysis and comparison.

Based on explicit data, collaborative filtering is one of the most valuable technologies of a recomender system. However, the further development of a recomender system has been restricted to some extent by the problems of cold start and data sparsity. To weaken the effect caused by data loss, some implicit feedback data are typically introduced into the recommendation such as social information and attribute data. In this paper, we propose a heterogeneous information boosting model for recommendations (HIBoosting). The model takes advantage of different network meta-paths to mine the potential information of user social networks, object metadata and interactive data in heterogeneous information networks. For different semantic information, we use a random-walk based on a meta-path to calculate the similarities of users or items, which are used to extract the low-dimensional embedded features of users or items by factorization, construct user profiles and item profiles. Finally, the embedded features are used for integrated learning by a gradient boosting decision tree (GBDT) to provide users with better recommendation services. The model not only integrates heterogeneous information in information networks, but also makes full use of mining latent relations of heterogeneous information networks. Experiments on the CiaoDVD and Lastfm datasets show that HIBoosting has made great progress in the accuracy of a recommender system.