A New Fuzzy Multiobjective Geometric Programming in Double Sampling in Presence of Non-Response

Abstract

Non-linear programming problems can be solved efficiently by geometric programming in which non-linear expressions can be expressed by an exponential or power functions. In this paper, Double Sampling Stratification (DSS) strategy is used in multivariate stratified population with unidentified strata weights, for optimum sampling design (OSD) in the presence of non-response to estimate the unidentified population means. The double sampling problem in the presence of non-response is formulated as Fuzzy Multiobjective Convex Programming Problem (FMOCPP). Then, we convert FMOCPP into Fuzzy Single Objective Convex Problem (FSOCP) by using membership function. Dual solution is obtained using LINGO Software by solving FSOCP. The optimum allocations of sample sizes of respondents and non- respondents for both the phases are obtained by applying dual solutions and primal-dual relationship theorem. The given technique is illustrated by projecting a numerical problem.

Keywords

• Double sampling
• dual solutions (DS)
• fuzzy programming (FP)
• geometric programming (GP)
• non-linear programming (NLP)
• non-response