Regular Similarity Relation On F(S) In Propositional Logic And An New Triple-I Method Of Fuzzy Reasoning

Since professor Zadeh firstly introduced a theory of approximate reasoning based on fuzzy sets and famous CRI method of fuzzy reasoning in 1973, it has witnessed great development. In particular, it has been successfully applied to fuzzy control. However, the theory of fuzzy logic is still not perfect; the method of fuzzy reasoning are still not very reasonable; and fuzzy logic and fuzzy reasoning are still not suitably combined. These not only have restricted further development of fuzzy logic but also inevitably have led to controversies over the reasonableness of fuzzy logic and fuzzy reasoning.In the past several years, on the joint research of fuzzy logic and fuzzy reasoning, a series of meaningful results have been obtained. An new formal deductive systemL* of fuzzy propositional logic was proposed in 1997; the triple I inference method of fuzzy reasoning was put forward in 1999. This method reasonably improved the conventional compositional rule of inference (CRI method for short) in fuzzy control; non-fuzzy versions of fuzzy reasoning in classical logics was built up in 2001.In addition, it is not the fact that approximate reasoning must keep in touch with fuzzy sets, the major part of approximate reasoning proposed by prof. Wang Guo-jun in his monograph <> is independent of the theory of fuzzy sets. Lately, base on the infinite product of evenly distributed probability spaces, prof. Wang proposed the theory of truth degrees in two-valued propositional logics.In the first part, let B be a Boolean algebra and be the set of all homomorphisms from B into {0,1}, and be a probability measure on . The concepts of sizes of elements of B and similarity degrees of pairs of elements of B by means of were defined and then a metric on B was deduced therefrom.In the second part, in two-valued propositional logic, the paper introduced the concept of regular similarity degrees of pairs of elements of F(S), and presented a kind of regular similarity degree by means of truth degrees. As an application, apseudo-metric on F(S) was deduced and proved that it is equivalent to two other pseudo-metrics on F(5).In the third part, the paper presented the rule of over-half credible and an new triple-I method of fuzzy reasoning named (Triple I)*. Furthermore, the formal deductivesystem L* of fuzzy prepositional logic and (Triple I)* were suitably combined bymeans of the root theory in L* .