On multivariate-multiobjective stratified sampling design under probabilistic environment: A fuzzy programming technique

Abstract

In a multivariate stratified sampling design, the individual optimum allocation of one character may not remain optimum to other characteristics. For the solution of such problems, a usable allocation must be required to get precise estimates of the unknown population parameters, which may be near optimum to all characteristics in some sense. The compromise criterion is required to obtain such usable allocation in sampling literature. In this paper, the sample allocation problem is considered as a stochastic nonlinear programming problem and thereafter formulated into a multiobjective programming problem to provide the usable allocation. The formulated problem is solved by using different models of stochastic optimization. Afterwards, the proposed allocation is worked out and compared with some other allocations, which are well defined in sampling, to give a comparative study. Also, the numerical study defines the practical utility of the proposed technique.