Abstract
Based on the definition of 2-dimension linguistic information of multiple attribute decision making problems proposed by Zhu, Zhou and Yang (2009), the information on evaluation is extended to 2-dimension uncertain linguistic variables, and a new method is proposed to solve the multiple-attribute group decision making problems in which the attribute values take the form of 2-dimension uncertain linguistic variables and the attribute weights are unknown. Firstly, the II class of uncertain linguistic information is transformed into the subjective weights of the experts, and then the subjective weights, the similarity degree of experts’ evaluation information and authority weights are aggregated to the comprehensive weights of each expert. By the comprehensive weights, the group decision making matrix is produced by weighting evaluation information of each expert. Then the maximum deviation method is used to calculate the attribute weights and TOPSIS method is proposed to rank the alternatives. Finally, an example is given to illustrate the decision-making steps and the effectiveness of this method.
Highlights
Multiple attribute decision making (MADM) has been extensively applied to various areas ranging from economics to engineering technology
Zhang et al (2007) studied the MADM problems in which the attribute value is the uncertain linguistic variables and the attribute weight is known, and proposed the UEWAA operator to aggregate the group decision making information and utilized the probability matrix ranking formula to rank the order of the alternatives; Zhang et al (2006) studied the multiple attribute group decision making problems in which the attribute values and attribute weights take the form of linguistic information, and proposed the ULWM operator to aggregate the comprehensive attribute values of the alternatives and ranked the alternatives based on ranking the fuzzy complementary judgment matrix
Cheng et al (2006) studied the multiple attribute decision making problems in which the information on evaluation is the uncertain linguistic information and the decision making matrix has some unknown values, and proposed a method which can fill the unknown values in linguistic decision making matrix and a method which can determine the comprehensive attribute weights based on attribute subjective and objective weights
Summary
Multiple attribute decision making (MADM) has been extensively applied to various areas ranging from economics to engineering technology. Wei et al (2007) studied the multiple attribute group decision making problems with uncertain linguistic information, in which the attribute weight and expert weight take the form of real numbers, and the preference value takes the form of uncertain linguistic variables, and proposed a new method based on the ULWGM and the ULHGA operators. Lk ij giUj k is the II class of the uncertain linguistic evaluation information, and it shows the subjective evaluation of the reliability of the decision results, and g and g are the element of the pre-defining linguistic evaluation set S2 = (s0, s1, , st−1) Based on these conditions, the order of the alternatives of multiple attribute decision making problems based on the 2-dimension uncertain linguistic variables can be ranked
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