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为了更好地解决决策者具有(严格)凸性偏好结构下的多目标决策问题,一般目标空间为有界凸域的情形常常可以转化为目标空间为有界闭凸区域的情形,首先分析了切割平面及该平面上偏好最优点与被切割平面分割成的为有界闭凸区域的目标空间或目标空间的子集的两个部分之间的关系;然后分析并指出了对于包含全局偏好最优目标方案点的为有界闭凸域的目标空间及其子集(准最优目标集),在确定了切割平面上的偏好最优点后,通过适当地选取供决策者与切割平面的偏好最优点进行比较判断的目标方案点,经过一次比较就可以确定一个新的范围更小的包含全局偏好最优目标方案点的目标空间的有界闭凸子区域(准最优目标集).为获取切割平面上的偏好最优点,提出了改进的坐标轮换法.在这些结论和方法的基础上,提出了决策者具有(严格)凸性偏好结构下的一类交互式多目标决策方法,要求决策者提供较易的偏好性息,决策效能较好.
In order to solve the multi-objective decision-making problem under the (strict) convex preference structure of decision-makers, the situation that the general target space is a bounded convex domain can often be transformed into a case where the target space is a bounded closed convex region. Firstly, The relationship between the cutting plane and the optimal point on the plane and the two parts of the target space or the subset of the target space which is bounded by the cutting plane and is partitioned by the cutting plane. Then, The optimal target point is the target space and its subsets (quasi-optimal target set) of bounded closed convex domains. After the optimal points of preference on the cutting plane are determined, by choosing the preferences of decision makers and cutting planes The best point to compare and determine the target program point, after a comparison can be determined by a new smaller area containing the global optimization of the optimal target program point bounded closed convex sub-region (quasi-optimal target set) The optimal point of preference on the cutting plane is obtained and an improved coordinate rotation method is proposed.On the basis of these conclusions and methods, a class of decision maker with (strict) convexity preference structure is proposed Interactive multi-objective decision making requires decision-makers to provide easier preference of information, decision-making performance better.