Characterizations And Applications Of Three Types Of Fuzzy Implications

As the generalization of classical implications, fuzzy implications, implications for short, have important applications in many fields such as fuzzy logic, fuzzy control, fuzzy expert system, fuzzy decision making and so on. The main research topics about implications include the following components: generation of new implications, discussion of properties and characterizations of different implications and intersections between different types of implications. From these studies about implications, we can deal with uncertain information better, expand the scope of applications of implications, lay the strict foundation for further development of uncertainty theory and application researches.In this thesis main topics and new contributions are as follows.Research on the D-implications. Based on the known results of D-implications, we further analyze properties of D-implications, study necessary and sufficient conditions under which a D-operation becomes a D-implication, discuss the conditions under which D-implication satisfies several important properties, including the exchange principle, identity principle, the ordering property and the left neutrality property.Research on the generalized g-generated implication. On the foundation of the known results about the g-generated implications, we propose a new type of implications, called the generalized g-generated implications. We give some examples of the generalized g-generated implications, study necessary and sufficient conditions under which two generalized g-generated implications are equal, discuss the conditions of the generalized g-generated implication satisfies some properties, research the continuity of the generalized g-generated implications.Research on the h-implications. We generalize the h-implications occurred in the literatures, and propose a type of new implications, called(h,f,g)-implications. We study necessary and sufficient conditions under which two(h,f,g)-implications are equal, discuss the basic properties of the(h,f,g)-implications, research the continuity of the(h,f,g)-implications.The law of importation for the above mentioned three types of implications is studied.At last, the above mentioned three types of implications are employed in fuzzy reasoning. At the same time, two examples about fuzzy reasoning are also given.