Sequential three-way decision (S3WD) is an efficient granular computing paradigm for dealing with uncertain problems. However, it is primarily oriented to all decision classes, which contradicts the fact that decisions are typically for the specific decision classes. Meanwhile, most S3WD models hide the topological structure of the granules, leading to difficulties in semantic interpretation. To address the issues, integrating model construction, attribute reduction and knowledge extraction, a general framework of granular sequential three-way decision for the specific decision classes is proposed to improve semantic interpretation and computational efficiency. First, a two-stage trisecting strategy and a GrS3WD model are proposed to integrate model construction with attribute reduction. Its main advantage is that it retains the topological structure of granules, which not only enhances semantic interpretation, but also avoids unnecessary double counting. Second, three acceleration strategies and a novel granular sequential three-way reduction (GrS3WR) algorithm are proposed to fast obtain a classification-based reduct or a class-specific reduct. Finally, the decision rules with multigranularity can be directly extracted from the concept tree generated by GrS3WR. Experimental results demonstrate that a class-specific reduct usually has fewer attributes and better classification performance than a classification-based reduct. Moreover, GrS3WR can significantly improve the computational efficiency of attribute reduction.

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.

In the process of decision making (DM), to have more freedom in expressing DM experts' belief about membership and nonmembership grade, Yager presented the q-rung orthopair fuzzy sets (q-ROFSs) as an extension of fuzzy sets. Recently, for aggregating discrete and continuous q-ROF information, many scholars provided various aggregation operators. However, there are still some kinds of continuous q-ROF information cannot be aggregated through existing aggregation operators. In this paper, we present two novel kinds of line integrals under the q-rung orthopair fuzzy environment (q-ROFE), which supply a wider range on method choice for multiple attribute decision making (MADM) concerning discrete or continuous q-ROF information. We first construct the first form of line integral under the q-ROFE and study their properties, we prove the specific condition mean valued theorem but negate the general condition for it. Besides, several inequalities with regard to it are also provided. After that, we give two characterization forms of the second form of line integral under the q-ROFE, we study the relationship between two kinds of line integrals. What is more important, we show the Green formula under q-ROFE, which connect the existing q-rung orthopair fuzzy integration theory. Afterward, we provide two kinds of aggregation operators on the basis of two line integrals, respectively. As their applications, we give two novel MADM methods based on two kinds of line integral aggregation operators. And some examples are shown to demonstrate the aggregation process of line integral operators. We not only stress their availabilities and superiorities on aggregating continuous q-ROF information, but also comparing with other existing aggregation methods for emphasizing the novel methods' abilities when deal with abnormal q-ROF information.