Interval-valued Fuzzy Reasoning

The scope of study and application of mathematics has extended from accuracy into fuzzy since Prof.Zadeh established fuzzy sets theory in 1965. Turksen proposed the interval-valued fuzzy sets in 1986. The membership function of interval-valued fuzzy sets was easier to assure than that of the fuzzy sets. Because its membership function contained not only the positive information of variable but also the negative information that accorded with the life, it provides more choices for the attribute description of an object and has stronger ability to express uncertainty than ordinary fuzzy sets. It has gained extensive attention in recent years and various fuzzy reasoning method have already put forward. This dissertation mainly studies various fuzzy reasoning methods, and a kind of new interval-valued fuzzy reasoning method is proposed on this foundation.The main results, obtained in this dissertation, may be summarized as follows:In chapter 1, an introduction was first given to the development of interval-valued fuzzy reasoning. Then the basis concepts of interval-valued fuzzy sets were reviewed.In chapter 2, interval-valued fuzzy reasoning theory and reductive property were studied. A definition that is satisfied the certain condition is proposed of the reductive property of interval-valued FMT with multiple rules. And then research on the existing fuzzy reasoning methods.In chapter 3, a kind of new interval-valued fuzzy reasoning method with the reductive property is proposed. The process of reasoning is illustrated with an example. The results show that the new method with the reductive property is a good fuzzy reasoning method.