The Optimal Solutions as Triple I Formula Taking the Minimal Value

Abstract:

      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.