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The TODIM (an acronym in Portuguese for interactive and multiple attribute decision making) method is a valuable tool to solve the multiple attribute decision making (MADM) problems considering the behavior of the decision maker (DM), while it cannot be used to handle the problem with unknown weight information on attributes, in this paper, a novel method based on the classical TODIM method is proposed to solve the hybrid MADM problems with unknown weight information on attributes, in which attribute values are represented in four different formats: crisp numbers, interval numbers, triangular fuzzy numbers and trapezoidal fuzzy numbers. Firstly, the positive-ideal alternative and negative-ideal alternative are determined, and the gain and loss matrices are constructed by calculating the gain and loss of each alternative relatived to the ideal alternatives concerning each attribute based on different distance calculation formulas, which may avoid the information missing or information distortion in the process of unifying multiform attribute values into a certain representation form. Secondly, an optimization model based on the maximizing deviation (MD) method, by which the attribute weights can be determined, is established for the TODIM method. Further, the calculation steps to solve the hybrid MADM problems are given. Finally, two numerical examples are presented to illustrate the usefulness of the proposed method, and the results show that the DM's psychological behavior, attribute weights and the transformed information would highly affect the ranking orders of alternatives. [ABSTRACT FROM AUTHOR]

Firstly, the research progress of grey model GM (1,1) is summarized, which is divided into three development stages: assimilation, alienation and melting stages. Then, the matrix analysis theory is used to study the modeling mechanism of GM (1,1), which decomposes the modeling data matrix into raw data transformation matrix, accumulated generating operation matrix and background value selection matrix. The changes of these three matrices are the essential reasons affecting the modeling and the accuracy of GM (1,1). Finally, the paper proposes a generalization grey model GGM (1,1), which is a extended form of GM (1,1) and also a unified form of model GM (1,1), model GM (1,1,α), stage grey model, hopping grey model, generalized accumulated model, strengthening operator model, weakening operator model and unequal interval model. And the theory and practical significance of the extended model is analyzed. [ABSTRACT FROM AUTHOR]