正则蕴涵算子分析性质的研究

Analytical properties of regular operator implication

针对正则蕴涵算子,从分析学的角度研究了其连续性.得到了正则蕴涵算子是连续函数的充要条件是当x≥y时,满足(x→y)→y=x;仅在(0,0)间断函数的充要条件是当x≥y,y≠0时,(x→y)→y=x,而对任意x∈(0,1),(x→0)→0≠x.同时研究了与这些蕴涵算子相伴随的三角模.

The basic analytical properties of regular implication are discussed. A regular implication is continuous if and only if it satisfies x≥y, （x→y）→y=x and it is continuous except the point （0,0） if and only if it satisfies x≥y and y≠0, （x→y）→y=x, while for all x∈（0, 1） （x→0）→0≠x. Furthermore the triangular norms which are a jointed with them is studied.