From the viewpoint of entropy, this paper investigates a hybrid multiple attribute decision making problem with precision number, interval number and fuzzy number. It defines a new concept： project entropy and the de...From the viewpoint of entropy, this paper investigates a hybrid multiple attribute decision making problem with precision number, interval number and fuzzy number. It defines a new concept： project entropy and the decision is taken according to the values. The validity and scientific nature of the given is proven.展开更多
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 decis...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.展开更多
文摘From the viewpoint of entropy, this paper investigates a hybrid multiple attribute decision making problem with precision number, interval number and fuzzy number. It defines a new concept： project entropy and the decision is taken according to the values. The validity and scientific nature of the given is proven.
基金supported by the Ministry of Education Project of Humanities and Social Sciences(13XJC630011)the Specialized Research Fund for the Doctoral Program of Higher Education of China(20130203120024)+1 种基金the Soft Science Project of Shaanxi Province(2013KRZ25)the Xi’an Science and Technology Plan Projects(SF1404)
文摘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.
