一种模糊概念格模型及其渐进式构造算法

A Fuzzy Concept Lattice Model and Its Incremental Construction Algorithm

传统形式概念分析方法无法处理现实中模糊和不确定信息,因此,对模糊概念格及其信息表示的研究具有重要意义.文中提出了一种模糊概念格模型,提出了模糊形式背景中属性隶属度值的窗口截取方法,定义了模糊概念的模糊参数σ和λ,给出了模糊概念格渐进式构造算法,推导出了模糊参数σ和λ的渐进式计算公式.模糊参数σ和λ分别体现了概念外延对于属性的隶属度的均值和发散程度.在模糊概念格渐进式构造算法中引入两个中间参数以实现模糊参数的渐进式计算.最后,进行了算法性能评估实验,结果表明模糊概念格的这种渐进式构造算法在时间上和空间上都具有良好的性能.

Classical formal concept analysis can not deal with the vague and uncertain information in practice. So the research on fuzzy concept lattice is an important task. This paper proposes a fuzzy concept lattice model, and suggests a method in which a select window is adopted for cutting the membership degrees in fuzzy formal context, two fuzzy parameters, a and it, are defined. Then this paper presents a new incremental algorithm to incrementally construct the fuzzy concept lattice by inserting new object one by one, and deduces several formulas about incrementally computing the fuzzy parameters, a and it. The two fuzzy parameters embody the average and the diffused degree of the membership degrees in a fuzzy concept respectively. In the incremental construct algorithm of fuzzy concept lattice, two interim parameters are introduced to carry out the incremental computation of the two fuzzy parameters. Experimental results on artificially generated datasets show that the construction algorithm has excellent performance on the time-spatial complexity.