| The scope of study and application of mathematics has extended from accuracy into fuzzy since Prof. Zadeh established fuzzy sets theory in 1965. The concepts of intuitionistic fuzzy sets (vague sets) and interval-valued fuzzy sets are two extensions of Zadeh's fuzzy sets. Jin Yingwei puts forward the fuzzy incomplete definition in 2003. Interval-valued fuzzy sets has been added to fuzzy incomplete definition in this dissertation, since fuzzy incomplete processes the information of membership and non-membership, it provides more choices for the attribute description of an object and has stronger ability to express uncertainty than Zadeh's fuzzy sets. It gains extensive attention from the academic circles and the circles of engineering and technology.The main results in this dissertation is as follows: firstly, it establishes a method of determining the objective weight in fuzzy incomplete multiattribute decision-making and two methods to get fuzzy incomplete weight, a new method let the fuzzy incomplete weight to be quantitative is also established. Secondly, it applies Projection and Gray Correlation Analysis to fuzzy incomplete multiattribute decision-making, and then combines the two theories' virtues to get the integrating decision-making method. Last part firstly summarizes the methods to value i, and suggests a new way to value i, also applying the new method to solve fuzzy incomplete Multiple Attribute Decision-Making problems. And after this, a new kind of method also with steps to solve mixed decision of multi attributes which includes fuzzy incomplete set has been found under the use of connection numbers' situation permutation principle. Every method is illustrated by examples in this part. And the demonstration and expectation are found in the end.
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