基于格值逻辑的模糊概念格

从逻辑的角度,将非经典逻辑之一的格值逻辑引入概念格,建立了格值模糊形式背景,通过格结构来刻画对象与属性之间的模糊关系,证明了由蕴涵算子诱导的算子对是伽罗瓦连接,并讨论了相关的一些性质,进而给出了格值模糊概念格的构造算法.格值模糊概念格的建立为模糊性与不可比较性信息的处理提供了可靠的数学工具.

Fuzzy Concept Lattice Based on Lattice-valued Logic

From the viewpoint of formal logic，a non-classical logic-lattice-valued logic is introduced into concept lattice. Lattice-valued fuzzy formal context is constructed and the fuzzy relation between attributes and objects is depicted through the lattice structure. The operator pair induced by implication operator is proved to be Galois connection and some relative properties are discussed, furthermore, the construction algorithm is given. The lattice-valued fuzzy concept lattice is a new mathematical tool to deal with problems on vagueness and uncertainty.