Compromise allocation problem in multivariate stratified sampling with flexible fuzzy goals

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.