CONTRAPOSITIVE SYMMETRY OF DISTRIBUTIVE FUZZY IMPLICATIONS

摘要

Recently, we have examined the solutions of the system of the functional equations I(x,T(y,z)) = T(I(x,y),I(x,z)), I(x, I(y,z)) = I(T(x,y),z), where T: [0,1]~2 → [0,1] is a strict t-norm and I: [0,1]~2 → [0,1] is a non-continuous fuzzy implication. In this paper we continue these investigations for contrapositive implications, i.e. functions which satisfy the functional equation I(x,y) = I(N(y),N(x)), with a strong negation N: [0,1] → [0,1]. We show also the bounds for two classes of fuzzy implications which are connected with our investigations.