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With respect to the problem of hybrid multiple attribute decision-making with incomplete information on attribute weights to which the attribute values are given in terms of precision number, interval number and fuzzy numbers, a new method is proposed. Firstly, the three different forms of numbers are unified into the form of interval number. The operational laws of interval numbers and a formula of possibility degree for the comparison between interval numbers, and then define the concept of deviation degree between interval numbers are introduced. An optimization model based on the maximizing deviation method, by which the attribute weights can be determined is established. The uncertain weighting average (UWA) operator is utilized to aggregate the interval numbers decosion making information corresponding to each alternative, and the formula of possibility degree is utilized to construct a possibility degree matrix (or called complementary judgement matrix), and then the priority formula of complementary judgement matrix is utilized to rank the alternatives and select the most desirable one(s). Finally, a numerical example is provided to illustrate the proposed method. The result shows the approach is simple, effective and easy to calculate.

The aim of this paper is to investigate the multiple attribute decision making problems with triangular fuzzy information, in which the information about attribute weights is completely unknown, and the attribute values take the form of triangular fuzzy numbers. In order to get the weight vector of the attribute, we establish an optimization model based on the maximum deviation, by which the attribute weights can be determined. Then, based on the traditional TOPSIS method, calculation steps for solving fuzzy multiple attribute decision-making problems with completely unknown weight information are given. The weighted distances between every alternative and positive ideal solution and negative ideal solution are calculated. Then, according to the weighted distances, the relative closeness degree to the positive ideal solution is calculated to rank all alternatives. Finally, a numerical example is provided to illustrate the proposed method. The result shows the approach is simple, effective and easy to calculate.

With respect to multiple attribute group decision making problems with linguistic assessment information, a new decision making analysis method is proposed. In the method, the two-tuple linguistic representation developed in recent years is used to aggregate the linguistic assessment information. An optimization model with minimizing deviation method based on the group ideal alternative, by which the attribute weights can be determined, is established. For the special situations where the information about attribute weights is completely unknown, another optimization model is established based on the group ideal alternative. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. We utilize the two-tuple linguistic weighting arithmetic average (T-WAA) operator to aggregate the linguistic information corresponding to each alternative in order to rank the alternatives and select the most desirable one(s). The method has exact characteristic in linguistic information processing. It avoided information distortion and losing which occur formerly in the linguistic information processing. Finally, a numerical example is used to illustrate the use of the proposed method. The result shows the approach is simple, effective and easy to calculate.

From among multiple criteria models in making complex decisions and multiple criteria models for the most preferable choice, grey relational analysis (GRA) approach has been dealt with. In some cases, determining precisely the exact value of the weight is difficult and that, as a result of this, their values are considered as intervals. Therefore, the aim of this paper is to extend the grey relational analysis to evaluate and select the best alternative for decision-making problems with interval weight. An algorithm to extend the grey relational analysis for MCDM problems to determine the most preferable choice among all possible choices, when weight is interval, is presented. Finally, an example is shown to demonstrate that the grey relational analysis result is a satisfactory and effective evaluation.

With respect to multiple attribute group decision making (MAGDM) problems in which the attribute weights take the form of interval numbers, and the preference values take the form of uncertain linguistic variables, by utilizing some operational laws of uncertain linguistic variables and a formula for the comparison between two uncertain linguistic variables. A new aggregation operator called interval geometric aggregation (IGA) operator is proposed and then an IGA operator-based approach to MAGDM in uncertain linguistic setting is developed. The approach is simple and effective. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.