Fuzzy Multiple Attribute Group Decision Making Based On 2-Dimension Linguistic Evaluation Information

Multiple attribute group decision making(MAGDM)problem plays important roles in modern decision making sciences,and it has been widely used in many fields including science and technology,culture,politics and so on.Consider complexity of objective things and the limitation of human thinking,decision makers(DMs)are tend to provide qualitative information when making evaluation,as a type of qualitative evaluation information,linguistic variables(LVs)can be used to express fuzzy information intuitively and expediently,therefore,the MAGDM with LVs has got a great deal of attention and has achieved fruitful researches so far.When DMs provide their linguistic evaluation information,there is such a kind of condition,that is,the DMs are required to give not only the attribute values of all the objects,but also the reliable judgement of each evaluation results,i.e.,the DMs provide the 2-dimension linguistic variables(2DLVs)to process linguistic decision-making prob-lems.The 2DLVs consist of two LVs:the first is an imprecise linguistic evaluation for an object or an attribute,and the second is to describe the reliability of the first one.Obviously,2DLV can more accurately reflect the evaluation of DMs on objects;thus,research on MAGDM problems based on 2DLV is of great theoretical and practical significance.The paper studies the theories and methods for 2-dimension linguistic MAGDM problems.The main work of this paper is summarized as follows:Chapter 1 focus on the implications for research of this paper,and analyses the current research status related to linguistic decision making,and then gives the main researchful and discussed problems of this paper.Chapter 2 introduces the MAGDM,linguistic variables and 2-dimension lin-guistic variables.In Chapter 3,in the case of trapezoidal fuzzy information environment,a new trapezoidal fuzzy similarity measure is proposed for the MAGDM problem of venture capital in which experts' weights and attributes weights are unknown.Moreover,two optimal models are constructed to derive their weights on the basic of minimization of the trapezoidal fuzzy similarity measure.Furthermore,an approach to MAGDM with the new trapezoidal fuzzy similarity measure is proposed.Finally,an example of venture capital is used to show the feasibility and validity of the proposed method.In Chapter 4,in line with MADM problem where the evaluation information is in the form of 2DLV,MADM methods including the TOPSIS and the TODIM based on 2DLV are proposed.To begin with,the ? dimension linguistic information in the 2DLV is quantified in these approaches,uncertainty of DMs' subjective risk attitudes are used to reflect then uncertainty of 2DLV as well,and then a mapping that transforms 2DLV into linguistic belief structure is proposed.To reasonably assign the weights of linguistic belief degrees,an allocation model of linguistic belief degrees is constructed,and the distance measure based on the constructed linguistic belief structure for 2DLVs is built as well,and then methods of fuzzy MADM on the basis of TOPSIS and TODIM are employed.Finally,a numerical example indicates that the proposed method is effective and feasible.In Chapter 5,with respect to MAGDM problem where the evaluation informa-tion is in the form of trapezoidal two-dimension linguistic numbers(T-2DLNs),a new similarity measure for T-2DLNs is proposed.The two optimization models are constructed to solve experts' weight and attributes' weight in MAGDM on the basis of maximizing similarity measure,and then a new MAGDM method via similarity measure for T-2DLNs is presented.Finally,a numerical example indicates that the proposed method is effective and feasible.In the end,the work of this paper is summarized and we look to the vista of future work.