三I表达式取最小值时的最优解

The Optimal Solutions as Triple I Formula Taking the Minimal Value

中文关键词:  $R_0$-算子  三I表达式  三I算法.

英文关键词:implication operator $R_0$  triple I formula  triple I method.

中文摘要:

      在本文中，针对蕴涵算子$R_0$,我们给出了当$A\rightarrow B$与$A^*(B^*)$给定时,求使三I表达式$(A\rightarrow B)\rightarrow(A^*\rightarrow B^*)$取最小值的全体$B^*(A^*)$之集的上确界(下确界)算法.并将上确界算法推广到多维多重的模糊推理中.从三I表达式取最值时求最优的$B^*(A^*)$的角度来看,本文是三I算法思想的延伸和完善.

英文摘要:

      In this paper, for implication operator $R_0$, a method which calculates the supremum (infimum) of set of $B^*(A^*)$ such that triple I formula $(A\rightarrow B)\rightarrow (A^*\rightarrow B^*)$ takes minimal value is given. Moreover, this method is generalized into the general form of FMP. As far as finding the optimal solution $B^*(A^*)$ such that triple I formula takes the maximal value or the minimal value is concerned, this paper extends and perfects the idea of triple I method.