Vague集上的逻辑运算

Logical Operations on Vague Sets

通过定义单位区间I的Vague域上的偏序关系,给出Vague集在一个格V(I)上的定义.由单位区间上连续的模糊三角模、否定算子和连续的模糊蕴涵算子,依据经典扩张原理构造V(I)上相应的Vague逻辑算子,并由此导出Vague集上交与并运算、补运算以及S-蕴涵和R-蕴涵运算的表示.总结Vague逻辑运算的一些性质,以期完善Vague集的理论体系,拓宽其在逻辑、语言与推理以及信息表达与处理等领域的应用.

By defining a partial ordering relation on the Vague domain of unit interval I, a definition of Vague sets on a lattice V（I） was given. Applying the classic extension principle, the corresponding Vague logical operators defined on V（I） were constructed with continuous fuzzy triangular norms, negator and continuous fuzzy implicators. The representations of the generalized intersection/union, complementary operation and implications on Vague sets were introduced in the context. Some basic properties of Vague logical operations were summarized. It enriches the conceptual framework of Vague sets, and will enlarge its applications on such fields as logic, linguistic and inference, as well as the information representation and processing.