Generalized Multiple Attribute Group Decision Making With Linguistic Information And Its Application

Multiple attribute group decision making with linguistic information owns deep theoretical and practical background, which has been extremely attracted in the fields of economy, public administration, engineeringand ecotope, etc. At present, there are three main problems in the studies of multiple attribute group decision making. Firstly, in the process of linguistic information aggregation, the existed algebra operations are not closed, i.e., by considering the current algebra operational laws of linguistic variables, there is a situation that the present linguistic information aggregation is constructed by sacrificing the good explanation of the aggregated results. Secondly, the attribute information considered by experts may be inconsistent, which can be concluded with the case that the attributes evaluated by different experts are not the same, because the experts might be affected by the limit of their knowledge category and speciality. Thirdly, group decision making owns the property of groupment, i.e., for one aspect, the group decision making is a cooperative process that all experts are gathered to make a group task, for the other aspect, there may exist conflict among experts for the reason that each expert may have his/her own interest. Thus, the group decision making is a group incident. Besides, since the development and perfection of the theory of computing with words, many types of linguistic information including linguistic term set,2-tuple linguistic variable, virtual linguistic variable, uncertain linguistic variable, fuzzy linguistic approach, hesitant linguistic variable and unbalanced linguistic variable, etc, have been proposed. Therefore, it’s of great theoretical meaning and practical value to study the existed problems and the solution of group decision making with different kinds of linguistic information. By studying the mentioned problems, we provide some feasible solutions for those problems. The main contents are listed as follows:(1) A new algebra operational laws for 2-tuple linguistic variable and uncertain linguistic variables based on Archimedean triangular norms (t-norm,s-norm) are defined. The most advantage of the proposed operations is closed, which has overcome the drawbacks of current operations in logic and explanatory ability. We have proved some theoretical properties of the developed algebra operations, including the commutativity, associative law and distributive law, etc. With the notions and properties, the Archimedean triangular norms based ordered weighted averaging operator and the Archimedean triangular norm based ordered weighted geometric averaging operator for 2-tuple linguistic variables and uncertain linguistic variables are put forward, the properties of such operators are also discussed. The concise formulas of such aggregation operators are obtained by using the mathematical induction. The real applications of the proposed new operation based aggregation operators in the multiple attribute group decision making have also been discussed.(2) To handle the situation that attribute information considered by the experts are not the same, the concept of generalized multiple attribute group decision making (GMAGDM) is proposed. The generalization of the introduced model is illustrated, i.e., the normal multiple attribute group decision making and multiple attribute decision making are two special cases of GMAGDM. By considering the complexity of GMAGDM, two decision procedures are given. Firstly, the GMAGDM with linguistic information is transformed into normal real valued multiple attribute decision making by using the TOPSIS method to the decision information provided by each expert, then the decision process can be continued with normal real valued multiple attribute decision making methods. Secondly, the expert weighting vector prior aggregation method and attribute weighting vector prior aggregation method are provided, respectively. It’s worth noting that the former can keep the unity of the weight information, while the later would be more feasible in real applications.(3) By combining the soft set theory and 2-tuple linguistic environment, and the fuzzy soft set theory and uncertain linguistic environment, respectively, the notions of 2-tuple linguistic soft set (2-TLSS) and uncertain linguistic soft set (ULSS) are proposed. The operations of the two soft sets are systematically studied, including the set operations, the logic operations and the algebra operations. Especially, by utilizing different kinds of closed algebra operations, the closed algebra operations of two soft sets are provided, which are further used to derive the aggregation process of soft sets. Thus, four linguistic group decision procedures are produced on the basis of extension of traditional group decision making with soft set and linguistic soft information aggregation processes.(4) The axiomatic definitions of linguistic entropy and uncertain linguistic entropy are introduced based on corresponding notions on fuzzy set and interval-valued fuzzy set. According to existed literatures, two formula of linguistic entropy are structured. One is using the entropy function and the other is utilizing the relationship between distance measure and entropy measure. In order to show its application in real problems, the linguistic entropy weighting method and the optimizing weighting method with entropy measures are given, two numerical examples are shown.(5) In order to deal with the groupment of group decision making, a new GMAGDM method via cooperative games is introduced by combing the cooperative games and group decision making. Therein, the definition of group decision error is firstly defined, which is then distributed among players (experts) by using the Shapley value method. An iterative algorithm to get the weighting information of GMAGDM based on Shapley is designed; the convergence and complexity of the algorithm are discussed. Next, the proposed algorithm is applied to the solution of GMAGDM with fuzzy linguistic preference relations, which give a new idea for solving such issues. The numerical study shows that our proposed method has fast rate of convergence and practical feasibility.