| The theory and application of fuzzy mathematics was based on fuzzy sets theory which was established by Zadeh in 1965, and famous CRI method for FMP was proposed by him in 1973. Then Wang Guo Jun set forth a new triple I method for the defect of CRI method. This new method is more reasonable and has better logic foundation. Polish put forward that the conjunction of interval analysis and fuzzy set method has better result in the early 1980's, so interval-valued fuzzy set (IVFS) was provided and was applied in fuzzy reasoning. In recent years, it has gained extensive attention and various fuzzy reasoning methods have been given. This text mainly studies the triple I method of interval-valued fuzzy reasoning, and points out that the fuzzy reasoning is a special interval-valued fuzzy reasoning on condition that the interval degenerates into point.The main results, obtained in this dissertation, may be summarized as follows:In the first chapter, an introduction is first given to the development, and some properties of implication operator and triangle norm are reviewed.In the second chapter, the basis concepts of interval-valued fuzzy sets are given, and a new definition of interval-valued implication operator and triangle norm is proposed, then some properties are proved.In the third chapter, the triple I method and its reversibility and the opposite direction triple I method of interval-valued reasoning are put forward, then the triple I restricting method of interval-valued fuzzy reasoning is discussed on the basis of some certain conditions. At last, the results show that the fuzzy reasoning is a special interval-valued fuzzy reasoning on condition that the interval degenerates into point.
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