区间数型多属性决策正交投影模型及其应用

A Orthogonal Projection Model for Multi-Attribute Decision Making with Intervals and Its Application

针对用TOPSIS法进行多属性决策时备择方案可能既与“理想方案”距离最近，又与“负理想方案”距离最近的不足，用正交投影代替TOPSIS法中的相对贴近度，建立了区间数型多属性决策正交投影模型．模型首先将“理想方案”平移至坐标原点后，转换为0向量，只用平移后的“负理想方案”计算正交距离，然后将区间数转换为n＋bi型联系数，根据联系数复运算排序得到最终决策结果．通过一个工程设计方案评价例子进行了计算分析，说明了模型的有效性．

With respect to problems, in which alternative solutions may be the closest to the ＂ideal solution＂, but also the ＂negative ideal solution＂ distance ,in multi-attribute deci- sion making with TOPSIS method, a kind of multiple attribute decision making model with interval, in wich orthogonal projection be used in place of the relative closeness of TOPSIS method, is put forward. In the first, the ＂ideal solution＂ is translated to the origin of coor- dinates, converted to the zero vector, to compute the orthogonal projection by the ＂negative ideal solution＂ only, then the interval number is converted to a＋bi type connection number, and the final decision results is get depend on the order of complex arithmetic of number connection. Finally, through a engineering design scheme evaluation example of calculation and analysis shows that the model is effective.