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

Shafiullah Shafiullah,Abdul Bari,Abdul R Beig,Mohd Tariq

doi:10.1109/access.2020.2973935

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.

Highlights

The problem of non-response is frequently experiencing in conveyance of the sample surveys
NUMERICAL EXAMPLE We have considered the data for given numerical from [7] and [8] for the illustration of our proposed procedure
In this paper we have considered double sampling problem in the presence of non-response which is formulated as Fuzzy

Summary

INTRODUCTION

The problem of non-response is frequently experiencing in conveyance of the sample surveys. Shafiullah et al.: New Fuzzy Multiobjective GP in Double Sampling in Presence of Non-Response the population with unstratification is strained and sampled units from each stratum are recorded to estimate the unidentified strata weights at first stage. The researchers have worked in multiobjective geometric programming problem and applied in different fields as: [46]–[60] and many. The research work in fuzzy geometric programming and fuzzy goal programming has been done by many authors in different fields for obtaining the solution of the problems Such as: [61]–[74] and many others. The given technique is illustrated by projecting a numerical problem

FORMULATION OF THE DOUBLE SAMPLING FOR

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METHODOLOGY

NUMERICAL EXAMPLE

CONCLUSION