Research On Truth Degree Of N-valued (?)ukasiewicz Propositional Logic System

In this paper,the different truth degree forms of formulas in n-valued(?)ukasiewicz propositional logic system are studied.Firstly,the definitions of t-truth degree,t-similarity and t-pseudo distance of formulas are proposed.The MP rule,HS rule and operational properties of t truth degree are proved,and the pseudo metric space is established on the basis of t pseudo distance.We prove the continuity of the logic operator?,?,?,?,(?),?with respect to the pseudo distanced_n in the logic metric space(F(S),d _n).Three different approximate reasoning modes are proposed in the logic metric space,and the equivalence of the three approximate reasoning modes is proved.Then,by using the method of randomization of assignment sets,the calculation forms of t-random truth degree,t-random similarity degree and t-random pseudo distance are given in(?)_n.The properties of t-random truth degree,such as MP rule,HS rule,intersection and union reasoning rule are proved,and the theoretical t-random divergence degree and t-random compatibility degree are proposed,we propose three different approximate reasoning models in t-random logic metric space,and prove the equivalence of the three approximate reasoning models.Then,in the n-valued(?)ukasiewicz propositional logic system,t-absolute truth degree of formulas is proposed,and the operational and reasoning properties of t-absolute truth degree are proved.On this basis,t-absolute similarity and pseudo distance are introduced,and the properties of pseudo metric space are discussed.It is proved that the operator?,?,?,?,?,?are continuous with respect to pseudo distance d_D in logic metric space(F(S),d _D).Finally,by using the induced function of propositional formulas,the concepts of?-t truth degree,?-t similarity degree and?-t pseudo distance of propositional formulas relative to local finite theory?under t connectives are given,and some basic operational properties of?-t truth degree,such as MP rule and HS rule,are demonstrated.