Research On Methods And Application For Interval-Valued Information Multi-Criteria Group Decision-Making

In many fields such as economy, management and military, decision-makers (DMs)need to make investment decision, economic benefits evaluation and other decision-making activities. With the expanding of enterprise scale and the diversified of enterprise development,the complexity of decision-making is increasing. Actually, it is meaningless for enterprises to rely on a single criterion to make decisions. Instead, a comprehensive analysis of the multiple and conflicting factors is needed. The multi-criteria group decision-making (MCGDM) is an activity that aims to sort alternatives by integrating opinions of multiple DMs based on conflicting criteria. With the increasing complexity of decision-making, it is difficult to rely on mathematical models to accurately depict objects. In fact, the information is usually given with the form of interval variables. Therefore, the study of interval-valued MCGDM has a strong theoretical significance. However, there are some deficiencies in the existing study of interval-valued MCGDM including ignoring the subjective judgment of DMs toward information and ignoring the correlation among criteria. In this paper, we study the problem of MCGDM under the interval-valued information environment, this study including the following contents:(1) In the interval-number information environment, this paper studies aggregation operators based on the utility function, which consider the subjective judgment of DMs in the aggregation process. Firstly, for the general utility function, this paper develops two operators with the penalty function based on the optimal generalized deviation model,namely the interval generalized weighted utility multiple averaging (IGWUM) operator and the interval generalized ordered weighted utility multiple averaging (IGOWUM)operator, and their properties are also studied. Then, this paper focuses on a concrete utility function, hyperbolic absolute risk aversion (HARA) function, which can respectively obtain power utility, exponential utility and logarithm utility by suitable adjustments of the parameters, and another new operator named as the interval generalized ordered weighted utility multiple averaging-HARA (IGOWUM-HARA)operator is proposed. Thereafter, a new nonlinear objective programming model to determine the IGOWUM-HARA operator weight is developed. Finally, a new approach for interval-valued MCGDM is developed based on the IGOWUM-HARA operator and the weight-determining model.(2) In the interval-valued intuitionistic fuzzy environment, this paper studies aggregation operators based on the Shapley function and the Hamacher algorithm, which consider the correlation among elements. Firstly, two new operators named as the generalized interval-valued intuitionistic fuzzy Shapley Hamacher averaging (GIIFSHA)operator and the generalized interval-valued intuitionistic fuzzy ordered Shapley Hamacher averaging (GIIFOSHA) operator are developed, and their excellent properties and special forms are discussed. Then, a new similarity measure of the interval-valued intuitionistic fuzzy numbers is developed and a weight-determining model based on the minimum similarity theory is proposed. Finally, a new approach for interval-valued intuitionistic fuzzy MCGDM is developed based on the two operators and the weight-determining model.(3) In the 2-dimension interval linguistic (2DIL) environment, this paper proposes two new aggregation operators. Firstly, a 2-dimension interval linguistic generalized power weighted average (2DILGPWA) operator is developed to overcome the defect of the 2-dimension interval linguistic averaging operator that fails to express the important of element. It is proved that the operator satisfies the idempotence and the boundedness.Then, to further satisfy the permutation invariant, a 2-dimension interval linguistic ordered weighted power averaging (2DILOWPA) operator is deduced. It is proved the 2DILGPWA and 2DILOWPA operator can be evolved into different aggregation operators. Subsequently, a new distance between 2-dimension interval linguistic variables is proposed. In addition, based on the principle of maximum cross entropy, the weight model is established. At last, a new MCGDM method based on the 2DILGPWA and the 2DILOWPA operator is proposed.(4) In the hybrid interval information environment, this paper presents a MCGDM method to solve interval numbers, interval-valued intuitionistic fuzzy numbers and 2-dimension interval linguistic variables simultaneously. First, to overcome the defects of current method, new relative entropy of interval number is proposed; then the projection of interval-valued intuitionistic fuzzy numbers and the expectation of 2-dimension interval linguistic variables are introduced to sort the interval-valued intuitionistic fuzzy numbers and 2-dimension interval linguistic variables, respectively. Afterward, the distance measure of TOPSIS is replaced by the similarity measure of interval numbers,the cross entropy measure of interval-valued intuitionstic fuzzy numbers and the improved distance of 2-dimension interval linguistic variables. Moreover, the weights of criteria and DMs are determined by the idea of maximum deviation and the similarity degree, respectively. Finally, based on the extended TOPSIS and the weight optimization model, a method to solve the hybrid interval MCGDM problem is proposed.This study makes up the shortage of the current researches on interval information MCGDM, and some case studies prove the effectiveness of the proposed method. This study also provides a new effective theory and method for interval information in the practice of MCGDM problems.