逻辑系统MTL(BL)的新的模式扩张系统GNMTL(GNBL)

New Schematic Extensions GNMTL(GNBL) of MTL(CL)

首先给出了Gdel非算子的一个重要性质:一个模糊逻辑系统中的非是Gdel非的充要条件是如果x*y=0,则xy=0。然后,基于Gdel非算子分别提出了逻辑系统MTL和BL的新的模式扩张系统GNMTL和GNBL。GNMTL(GNBL)是基于一类左连续t-模(连续t-模)(都包含乘积t-模及Gdel t-模)的模糊逻辑的共同形式化;最后,分别给出了著名逻辑系统Gd与Π分别作为GNMTL和GNBL的模式扩张形式,同时给出了Gdel逻辑系统的几种等价形式。

First, we give an important property of Godel negation , which is that a negation operator in the fuzzy logic system is Godel negation iff if x ＊ y = 0, then xy = 0. And then, two new schematic extensions of MTL, GNMTL and GNBL, are introduced based on Godel negation, and they are formulation of fuzzy logic to handle a sort of left-continuous t-norms（containing Godel t-norm and product t-norm）. Finally, the schematic extensions of famous logic system God and Ⅱ of GNMTL and GNBL are given respectively, meanwhile, several equivalent forms of Godel logic system are given.