Study On Fuzzy Implication And Its Application

As an important connective,fuzzy implication is defined by its monotone properties and boundary conditions,and plays an important role in many fields such as fuzzy decision making,fuzzy control and so on.Many research results about properties and applications of fuzzy implications have been reported in the literature.In fuzzy control,based on the fuzzy rules,for arbitrary input values,output control conclusions can be obtained by fuzzy inference mechanism.One of the core technologies of the fuzzy inference mechanism is using appropriate fuzzy implication.In this thesis,we mainly study the methods of generating fuzzy implications;several new methods for generating implications by combining multiple implications are proposed;and consider applications of fuzzy implication in fuzzy reasoning.The main contents and conclusions of this thesis are as follows.This thesis presents three new methods for generating fuzzy implications.That is,new functions are generated by using some selected fuzzy implications for multiple iterations.After analysing,we find that these new functions are fuzzy implications when the original fuzzy implications have some designated properties.Furthermore,we analyze whether the resulting multiple fuzzy implications still maintain some properties when the original fuzzy implications have these properties.Also,we discuss when the mutual exchange law and logical tautologies are retained under the multiple operations.Some necessary and suffi-cient conditions are given under which these logical identities are satisfied by the derived implications.Next,the proposed multiple fuzzy implications are applied to full implication inference algorithm of fuzzy reasoning,thus we get the triple I solutions by using multiple fuzzy implications.Finally,inspired by the triple I method,we propose a fuzzy similarity reasoning algo-rithm based on full implication algorithm and the concept of fuzzy similarity.The solutions of fuzzy modus ponens and fuzzy modus tollens are derived.These results will provide new support for applications of fuzzy implications in fields,such as control theory and decision making.