| With the development of society, more and more information is well known to all. Some of the information is very valuable; even it is vital to your eventual decision. But more information only confuse your judgment. At that time, we need an excellent tool to aggregate so much information accurately. This paper introduce a kind of tool — aggregation operator. At first, we show some frequently-used aggregation operators which can aggregate four kinds of arguments, that is, actual numbers, fuzzy numbers, interval numbers and linguistic numbers. Secondly, based on the first part, many good properties of several kinds of generalized operators have been studied.However, the same problem is almost involved while aggregating information by using these operators. How to obtain the weights of operators? At present, international experts investigate the issue of obtaining operator weighs and have some good results. This paper exemplifies the methods of obtaining OWA operator weights and studies the kernel of this problem. On the basis of summarizing some others' methods, I investigate the properties and applications of a special geometric proportional weights. Meanwhile, I give an example to show the difference among the six methods. Due to the rapid development of forecasting and decision-making, people attempt to apply the operators to this wide area, which makes the operator theory more complete. At last, two examples are introduced to exhibit the applications of IOWA operator and LOWA operator in forecasting and decision-making. We can see from the examples that the aggregation operators are very useful tools and it is easy to practice. |
