有限内存空间下大规模模糊概念格快速构造理论与方法研究

Fuzzy concept lattice effectively extends information processing capacity of the formal concept analysis method, and therefore can be used in many application fields of traditional formal concept analysis. Most of fuzzy formal concept analysis application tasks need to construct fuzzy concept lattices. Due to the inherent properties of fuzzy concept lattices, its constructing process has exponential time complexity and space complexity. The existed methods for constructing fuzzy concept lattice are not suitable to build large-scale fuzzy concept lattices in practical applications, neither fit the diversity of computing environments. This project considers the problem of constructing fuzzy concept lattice as research contents, and take constructing large-scale fuzzy concept lattices in the limited memory space as our research goal. Therefore we deeply study and discuss this scientific issues from three points, which are (1) research on theories and algorithms of rapid construction; (2) research on theories and algorithms of partially construction and integration; (3) research on theories and algorithms of large-scale parallel construction. Algorithms from our research are integrated and published in the form of software component, that can provide basic supports to fuzzy formal concept analysis-based application tasks. This project's outputs to be an effective solution to constructing large-scale fuzzy concept lattice. Furthermore it can be applied in the practice of social production to produce more long-term social and economic benefits.

模糊概念格有效地扩展了形式概念分析方法信息处理能力，因此可应用于诸多传统形式概念分析应用领域。大多数基于模糊形式概念分析应用任务都是以模糊概念格构造为基础。而模糊概念格固有属性使得其构造过程具有指数级时间复杂度与空间复杂度。传统的模糊概念格构造模式，在实际应用中并不适用于大规模模糊概念格构造；更不适应多样性的计算环境。本项目以模糊概念格构造为独立研究内容，以有限内存空间下的大规模模糊概念格构造为研究目标。从①快速构造理论与算法研究；②分块构造与集成理论、算法研究；③大规模并行构造理论与算法研究；三个方面对该科学问题进行深入研究和探讨。研究取得的算法以软件构件的形式集成与发布，为基于模糊形式概念分析应用任务提供基础算法支持。本项研究成果能够有效解决实际应用中的大规模模糊概念格构造问题，与社会生产实践相结合，产生更加长远的社会与经济效益。

大多数基于模糊形式概念分析应用任务都是以模糊概念格构造为基础，而模糊概念格固有属性，使得其构造过程具有指数级时间复杂度与空间复杂度。本项目以模糊概念格构造为独立研究内容，以有限内存空间下的大规模模糊概念格构造为研究目标。从四个方面：①快速构造理论与算法研究；②分块构造与集成理论、算法研究；③大规模并行构造理论与算法研究；④基于概念格的应用，分别对该科学问题进行深入研究和探讨，达到了研究目标，取得了阶段性的成果。尤其子课题“快速构造理论与算法研究”，从模糊概念格完备格构造的基本理论，模糊概念格的渐增、渐减维护，用户“所构造即所需”的实用角度，概念格二元关系消减情况下的维护，以及三元概念的构造等多方位进行阐释；并且取得了基于模糊集合并、交运算构造方法的重要研究成果。在子课题“分块构造与集成理论、算法研究”中，实现了基于集成方法的模糊概念格构造的重要研究成果。在子课题“大规模并行构造理论与算法研究”中，实现了基于负载均衡的模糊概念并行构造的重要研究成果。这些工作完善了模糊概念格直接构造体系，实现了批处理、渐进、集成及并行化多种方式的构造，丰富了概念格维护的理论和方法，为基于形式概念分析应用任务提供了基础算法支持，能够有效解决实际应用中的大规模模糊概念格快速构造问题。本项目又进一步开展转化理论成果工作，将构造理论应用于多种基于概念格的应用中，与实践相结合，产生更加长远的社会与经济效益。