Linguistic Information Aggregation Operator And Its Application In Multi- Attribute Group Decision Making

In real life, people often encounter a variety of decision problem. Since the decision problems are very complexity, when people describe the object, they would rather use qualitative linguisic information to express their preferences. To manage the MAGDM problems under the linguistic invironment, the methods are mainly include as follows:approximate model based on extension principle, ordered linguistic calculating model,2-tuple semantic calculating model etc. The fuzzy operation base on extension principle will increase the degree of the fuzzy in the results, which may lose the linguistic information or change the linguistic information. In the process of ordered linguistic information calculating model, as the initial linguistic evaluation set is not continuous, when finish aggregating the linguistic information, it is hard to obtain the initial linguistic evaluation information. Although the accuracy is higher than other algorithms by using the 2-tuple semantic calculating model, it may not correspond to the initial number when the linguistic scales are non-equidistant. To avoid the bad situation of the three methods, the thesis takes MAGDM problems as the research backdrop, proposes a new kind of linguistic information qualitative aggregation operator, the aggregation operator make certains the aggregation results are still in the initial linguistic evaluation set, also guarantees the linguistic information calculation precision, and will not bring about counter intuitive problem. The main research contents of this thesis are showed as follows:In this thesis, a new qualitative operator to deal with the linguistic MAGDM problems is presented. First, a distance measure between two linguistic terms is defined, base on the distance measure, a new qualitative operator is proposed and its relative properties are studied. And consider that by using the new operator for aggregating linguistic information may lead to information lost, then a binary relation is proposed. In the binary relation, there are two parts, include the result of aggregation operator, and the number support order. To manage the linguistic MAGDM problems, which the experts’weights are completely unknown, base on the smaller difference, the larger similarity, the expert should be given a larger weight. The similarity between two decision preference matrices is defined, then the experts’weights are obtained. Consider that the method for obtaining the experts’weights is too ambiguous, a new way of obtaining the experts’weights is given. By using the new qualitative operator, the group opinions are achieved consensus, and the MAGDM problems change into MADM problems. If the attribute weights are not given, according to the larger difference of attribute have greater effection in the ranking, and the attribute should be given the larger weight. According to the numerical support order and attribute weight, the scores of the alternatives in the group opinions will be sorted, and the optimal alternative will be found. Finally, three methods of obtain the experts’weights are given, and a living example is given in detail to illustrate the availability of the new operator.