Studies On Construction Methods Of Fuzzy Implications

As a kind of important logic operator,fuzzy implications have been widely used in many fields,such as fuzzy reasoning,fuzzy control,fuzzy image processing,computing with words,fuzzy mathematical morphology,data mining and so on.Because of its theoretical significance and application value,the research of fuzzy implications have attracted much attention in recent years.The main research direction focuses on the construction methods of fuzzy implications,analysis and characterization of fuzzy implications as well as the relationship between fuzzy implications and functional equations.This thesis will propose some new construction methods of fuzzy implications,and study the properties of the new fuzzy implications along with the conditions when they satisfy some function equations.The main content of this thesis are as follows:Vemuri and Jayaram proposed two kinds of composition methods of fuzzy implications.But the two methods do not preserve the order properties and contrapositive symmetry.In order to make up for this shortage,we present a novel composition method of fuzzy implications and its generalization.Prove that these two methods preserve the order properties and contrapositive symmetry.The other basic properties of the new two kinds of fuzzy implication obtained by our methods are discussed.By using a set of strictly increasing sequences in(0,1),we make a meaningful generalization of the horizontal e-threshold generation method and the vertical e-threshold generation method of fuzzy implications.We refer to these two methods as horizontal multi-threshold generation method and vertical multi-threshold generation method of fuzzy implications.Some properties of the fuzzy implications generated by horizontal multi-threshold generation method and vertical multi-threshold generation method are given and their characterization are carried out.The relationship between the fuzzy implications generated by horizontal multi-threshold generation method and some functional equations are discussed.We present several new methods of contrapositivisation of fuzzy implications by using tnorms,t-conorms and fuzzy negations.These methods are called the(T,N)-contrapositivisation,(S,N)-contrapositivisation and(T,S,N)-contrapositivisation of fuzzy implications,respectively.When N is a strong negation,the three kinds of fuzzy implications obtained by these three methods are all have contrapositive symmetry.In addition,the other properties of these three kinds of new fuzzy implications are discussed in detail.Taking into account of those fuzzy implications that do not satisfy identity principle and ordering property,we propose two methods to modify the fuzzy implications.The modified fuzzy implications satisfy these two properties.We also consulted which properties are preserved by the modified fuzzy implications.