Two-Stage Stratified Randomized Response Model with Fuzzy Numbers

We consider an allocation problem in two-stage stratified Warner’s randomized response model and minimize the variance subject to cost constraint. The costs (measurement costs and total budget of the survey) in the cost constraint are assumed as fuzzy numbers, in particular triangular and trapezoidal fuzzy numbers due to the ease of use. The problem formulated is solved by using Lagrange multipliers technique and the optimum allocation obtained in the form of fuzzy numbers is converted into crisp form using α-cut method at a prescribed value of α. An illustrative numerical example is presented to demonstrate the proposed problem