In a multivariate stratified sample survey, we assumed p-characteristics which are to be measured on each unit of the population and the population is further subdivided into L subpopulations. For estimating the p-population means of all characteristics, which are not known in advance usually, a random sample is taken out from the population with the help of simple random sampling. In a multivariate stratified sample survey, the optimum allocation of one character is not considered as optimum for others. Then a solution is needed to work out an allocation that may be optimum for all characteristics in some sense, called as compromise allocation in sampling literature. The estimation of p-population means in the presence of non-response, for a fixed cost, is discussed. The formulated integer non-linear programming problem is converted into a binary goal programming problem. The problem's solution is obtained by using the concept of flexible fuzzy goal programming.

中文翻译：

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具有灵活模糊目标的多元分层抽样中的折衷分配问题

在多元分层抽样调查中，我们假设 p 特征将在每个人口单位上进行测量，并且人口进一步细分为 L 个子人口。为了估计通常事先未知的所有特征的p-总体均值，在简单随机抽样的帮助下从总体中随机抽取一个样本。在多元分层抽样调查中，一个角色的最佳分配不被认为是其他角色的最佳分配。然后需要一个解决方案来计算出在某种意义上对所有特征都可能是最佳的分配，在抽样文献中称为折衷分配。讨论了在固定成本的情况下对 p 总体均值的估计。将公式化的整数非线性规划问题转换为二元目标规划问题。问题的解是利用柔性模糊目标规划的概念得到的。