Abstract: In the field of Formal Concept Analysis (FCA), the proposal of concept sets satisfies the recommendation needs of real environments. At present, concept sets generation methods lack effective means to avoid the inclusion of redundant attributes, which to some extent affects the quality and efficiency of concept generation, and ultimately the effectiveness of recommendations. To solve the above problem, a Formal Context Attribute Reduction Algorithm (FCAR), a Concept Set Construction Algorithm (CSCA), and a Recommendation Algorithm Based on Concept Set (RACS) were proposed. Firstly, the attribute interest degree was designed based on the formal context and rating matrix, and the formal context reduction was achieved according to the threshold of attribute interest degree. Secondly, by combining extent similarity and intent interest degree, the concept criticality was designed as heuristic information to generate the concept set. Finally, the recommendation matrix of the concept set was obtained using the recommendation confidence and recommendation threshold, enabling personalized recommendations for the target user. The RACS algorithm is compared with kNN, IBCF, and formal concept recommendation algorithms GRHC, CSPR, and GreConD-kNN on 11 datasets. In experiments based on six standard datasets, the RACS algorithm achieves the highest accuracy and the second highest recall on three different datasets, and it achieves the best F1 score on four datasets. Especially on three larger-scale datasets, compared to formal concept recommendation algorithms, its average recommendation time efficiency is improved by nearly 59 times. The experimental results validate the significant advantages of the RACS algorithm in recommendation effectiveness and efficiency.

Key words: Formal Concept Analysis (FCA), reduced formal context, attribute interest degree, concept construction, recommendation system

摘要： 在形式概念分析(FCA)领域，概念集合的提出满足了真实环境的推荐需求。目前概念集合生成方法缺乏有效的手段避免冗余属性的参与，这在一定程度上影响了概念生成的质量和效率，最终影响了推荐的效果。针对上述问题，提出形式背景属性约简算法(FCAR)、概念集构造算法(CSCA)，以及基于概念集合的推荐算法(RACS)。首先根据形式背景和评分矩阵设计属性兴趣度，根据属性兴趣度阈值实现形式背景约简；其次结合外延相似性与内涵兴趣度，设计概念关键度作为启发信息，生成概念集合；最后利用推荐置信度与推荐阈值得到概念集的推荐矩阵，针对目标用户实现个性化推荐。RACS在11个数据集上与kNN、IBCF以及形式概念推荐算法GRHC、CSPR、GreConD-kNN进行对比实验。基于6个常规数据集的实验中，RACS在不同的3个数据集上表现出最高的精确度和次高的召回率，在4个数据集上F1值最优；尤其是在3个较大规模的数据集上，与形式概念推荐算法相比，其平均推荐时间效率提升了近59倍。实验结果验证了RACS在推荐效果和推荐效率上的显著优势。

关键词: 形式概念分析, 约简形式背景, 属性兴趣度, 概念构造, 推荐系统