(T,N)-implication And (f,g,u)-implication And Their Descriptions

Fuzzy logic was first established by L.A.Zadeh in 1967 which is an important branch of non-classical mathematical logic.It is also the foundation of reasoning mechanism in many fields such as information science and AI.Fuzzy implication is a generalization of Boole implication operator called Boole in fuzzy logic.It can not only explain fuzzy conditional proposition,but also describe reasoning process.Meanwhile,it also has many applications in fuzzy control,fuzzy inclusion mea-sure and image processing.In this thesis,on one hand,we introduce a new class of fuzzy implications called(T,N)-implications,and study some of their proper-ties,and discuss the characterizations of subclasses of(T,N)-implications.Then,we discuss the distributive equations of(T,N)-implications over t-norms and t-conorms.At last,we study the relationships of(T,N)-implications to f-implications,g-implications,(S,N)-implications and R-implications.On the other hand,we gen-eralize g-generated implications and get a new class of fuzzy implications called(f,g,u)-implications,which is the promotion of(g,u)-implications.Then,we dis-cuss the properties and the characterizations of subclasses of(f,g,u)-implications.Finally,we investigate the convex combination of(f,g,u)-implications.The struc-ture of this thesis is organized as follows:In the first chapter,basic concepts in fuzzy implication.In this chapter,some basic concepts and relevant conclusions such as fuzzy implication,triangular norm,triangular conorm,fuzzy negation,will be used in this paper are given.In the second chapter,(T,N)-implications and its basic properties.Firstly,we introduce the new class of fuzzy implications called(T,N)-implications,and study some of their properties,and discuss the characterizations of subclasses of(T,N)-implications.Secondly,we discuss the distributive equations of(T,N)-implications over t-norms and t-conorms.At last,we study the relationships of(T,N)-implications to f-implications,g-implications,(S,N)-implications and R-implications.In the third chapter,(f,g,u)-implications and its properties.Firstly,we gen-eralize g-generated implications and get a new class of fuzzy implications called(f,g,u)-implications,which is the promotion of(g,u)-implications.Secondly,we dis-cuss the properties and the characterizations of subclasses of(f,g,u)-implications.At last,we investigate the convex combination of(g,g,u)-implications.