A fuzzy goal programming approach in stochastic multivariate stratified sample surveys

This paper deals with fuzzy goal programming (FGP) approach to stochastic multivariate stratified sampling with non linear objective function and probabilistic non linear cost constraint which is formulated as a multiobjective non linear programming problem (MONLPP). In the model formulation of the problem, we first determine the individual best solution of the objective functions subject to the system constraints and construct the non linear membership functions of each objective. The non linear membership functions are then transformed into equivalent linear membership functions by first order Taylor series at the individual best solution point. Fuzzy goal programming approach is then used to achieve maximum degree of each of the membership goals by minimizing negative deviational variables and finally obtain the compromise allocation. A numerical example is presented to illustrate the computational procedure of the proposed approach.