研究函数方程组I(x,T(y,z))=T(I(x,y),I(x,z)),I(x,y),)=I(N(y),N(x))的解,其中T:[0,1]^2→[0,1]是一个严格三角模,I:[0,1]^2→[0,1]是一个模糊蕴涵算子和N:[0,1]→[0,1]是一个强否定。在,除了在点(0,0),(1,1)不连续的假设下,获得了满足这个函数方程组解的完全刻画。
In this paper, we explore the solution of functional equations I(x,T(y,z) ) = T(I(x,y),I(x,z)) and I(x,y) = I(N(y),N(x)), where T is a strict t-norm, I a fuzzy implication and N a strong negation. Under the assumptions that I is continuous except the points (0,0) and (1,1), we get the full characterizations of the solutions for both functional equations.