Each Other Along With Triangular Norms And Implication Operator And Implication Operator Approximation Problem

Triangular norms by which logic "and" can be shawed well play aimportant role in fuzzy logic. Meanwhile, the choice of implication opeators isclosely related to the effect of fuzzy reasoning. Therefore to research the triangularnorm and implication operator which are adoint reciprocally has a important andwide sense. In first section the sufficent and necessary conditions of the ajoint t ─norm and implication are given. Furthermore the problem of converging to somediscontinuous implication operators by a sequence of continuous implication opera-tors is studied in section two, especially the Ro- implication operator brought up byprofessor Wang Guojun. In section three, the formal systyms (?) of popitionalcalculus based on the residuated lattice which satisfies a (?) b =(?)(a�'(?)b) is es-tablished and the semantic theory and [F] completness are discussed. Finally I givethe sufficient condition that Ro ─ algebra can be reresented by Ro ─ implicationand study the congruence relationship on Ro ─ algebra.