Linguistic Multiset And Its Application In Multi-Attribute Group Decision Making

In the real life, multi-attribute group decision making problems have been extensively applied to many areas such as service industry、finance、 manufacturing industry and so on. For traditional multi-attribute group decision making problems, decision makes are used to expressing their preferences on alternatives with numerical values. However, because of being fuzzy and uncertain on the inherent vagueness of human preference as well as the objects, it is more acceptable for people to provide their preferences by means of linguistic terms. Therefore, it is of both academic and realistic value to study the multi-attribute group decision making problems under linguistic environment. In this thesis, we study on the linguistic multi-attribute group decision making problems based on the linguistic multiset, the main contents are as follows:(1) A new linguistic multiset is proposed and its order relation is studied. A conversion relationship between the values in interval [0,g] and the elements on the linguistic multiset is developed.(2) Based on the distance measure between the linguistic variables, a similarity measure between the linguistic variables is developed. Based on the similarity measure, a new method to determine the weights of experts about each alternative with respect to each attribute is proposed.(3) Based on the conversion relationship and the distance measure, a new linguistic aggregation operator ψ is proposed and its properties are studied. The operator ψ can deal with the linguistic variables with no-equidistant labels and avoid the directly calculation between numerical values and linguistic variables. Moreover, the aggregation results are expressing by the elements on the linguistic multiset which have clearly semantic.(4) For the linguistic multi-attribute group decision making problems, a linguistic multi-attribute group decision making method is developed based on linguistic multiset and an illustrative example is given to show the feasibility and applicability of the proposed method.