Stduy Of Triple I Method In Fuzzy Reasoning

The rule of fuzzy modus ponens (rule of FMP for short) was firstly proposed by Zadeh in 1973, and was developed by Mamdani. CRI method which was widely used came into being. Since then, fuzzy control technology based on the method of fuzzy reasoning is widely used in industry areas with significant economic profit. CRI method which has no obvious logical character only depends on numerical calculation, so it has not been accepted in artificial intelligence. Professor Wang Guo-jun has proposed the famous full implication triple I method, the basic idea as follows: for A( x )∈F ( X ), B ( y )∈F (Y ) and A~* ( x )∈F ( X )( B ~*( y )∈F (Y )), finding the best B ~* ( y )∈F (Y )( A~* ( x )∈F ( X)) such that A( x )→B ( y) sustain A~* ( x )→B ~*( y), where F ( X ) and F (Y )denote all fuzzy subsets on X and Y respectly. Full implication triple I method can improve classical CRI method effectively, and bring fuzzy reasoning into fuzzy logic. Since then, triple I methods in fuzzy reasoning were studied greatly in areas of fuzzy logic, fuzzy reasoning, fuzzy control. Song Shi-ji proposed the Triple I constraint method, the basic idea as follows: for A( x )∈F ( X ), B ( y )∈F (Y ) and A~* ( x )∈F ( X )( B ~*( y )∈F (Y )), finding the maximum B ~*( y )∈F (Y )(minimum A~* ( x )∈F ( X)) such that ( A( x )→B ( y))→( A~* ( x )→B ~*( y)) attends its minimum value, this improved and developed the theory of triple I method.In fuzzy reasoning, the result of reasoning is related to fuzzy implication operators either in CRI method or in full implication triple I method. The result is not equivalent by using different implication operators in reasoning. There is some adventure in application in fuzzy reasoning. Wang Guo-jun and Wu Wang-ming have proposed implication operator with parameter respectively, Zhang Xing-fang has proposed family of implication operators L -λ- Gand L -λ- R0. Therefore, we want to use implication operator with parameter to prevent adventure in fuzzy reasoning.Based on the thought of family of implication operators with parameter, triple I method in fuzzy reasoning are studied in this paper. The thought of family of implication operators is used in the study of triple I method. Peculiarly, based on family of implication operators L -λ- R0 which was proposed by professor Zhang Xing-fang, Triple I Constraint method and reverse Triple I Constraint method with respect to FMP and FMT models are studied, the formulas of finding the solutions of A~* ( x )and B ~*( y ) and strict proof are given. For formulas of A~* ( x )and B ~*( y ) contain parameterλ, the proper parameterλis chose to adapted different fuzzy reasoning in practice. The main results are as follows:Firstly, based on family of implication operators L -λ- R0, Triple I Constraint method andα-Triple I Constraint method with respect to FMP and FMT models are discussed.Secondly, based on family of implication operators L -λ- R0, reverse Triple I constraint method and reverseα-Triple I constraint method with respect to FMP and FMT models are discussed.Thirdly, IIP system is logic system to handle the family of continuous t-norms T p - II and their family of residua implication operators R p - II is proved, and the equivalency of system IIP and II is proved. Triple I Method andα- Triple I Method under the family of implication operators R p - II are discussed.Fourthly, the definitions of the family of continuous t-norms T p - L and their family of residua implication operators R p - L and logic system LP are given, the equivalent of logic system LP and logic system L is proved, and Triple I Method andα- Triple I Method under the family of implication operators R p - L are discussed.