三参数区间灰数信息下的决策方法

基于灰色系统理论的思想和方法，探讨了方案指标值为区间灰数且灰数取值可能性最大数已知的决策问题.首先定义了三参数区间灰数，利用这类灰数的特性及经典灰色关联决策的优势，提出了三参数灰色区间关联度方法；其次考虑到各方案的效果评价向量与理想最优方案及临界方案在空间位置及几何形状的接近度和相似性，构建了三参数灰色区间斜率关联系数公式，结合建立的三参数灰色区间关联系数公式，给出了灰色区间综合贴近度方法.最后借助三参数区间灰数评价值的期望值及一维投影寻踪法的分析技巧，引入了投影指标函数方法.并对上述三种决策方法建立了相应的算法，应用实例说明了文中提出的决策方法的合理性和有效性.为灰色决策理论与应用研究提供了新的思路.

Decision-making methods with three-parameter interval grey number

Based on grey system theory, the decision-making problem is discussed, in which the attribute values are interval grey numbers and the maximum probability of the value of grey number is known. Firstly, three-parameter interval grey number is defined,and the method of three parameters grey interval incidence degree is presented by using the characteristic of this kind of grey number and the advantage of classical grey incidence decision-making. Secondly, considering the proximity and comparability of space position and geometry shape among every scheme's effect evaluation vector, ideal project and critical project, we construct the three-parameter grey interval slopeincidence coefficient formula. Integrated with the above three-parameter grey interval incidence coefficient formula, the method of the grey interval synthesis close degree is given.Finally, by using the analytical technique of the expectation value of three-parameter interval grey numbers and projection pursuit algorithm, the projection attribute function method isintroduced. In addition, the corresponding algorithms of the above three methods are given. An example is used to demonstrate the rationality and validity of the proposed decision-making algorithms. A new approach is provided for the grey decision-making theory and its application.