In this paper, we applied an Interactive Fuzzy Goal Programming (IFGP) approach with linear, exponential and hyperbolic membership functions, which focuses on maximizing the minimum membership values to determine the preferred compromise solution for the multi-response stratified surveys problem, formulated as a MultiObjective Non Linear Programming Problem (MONLPP). | Yugoslav Journal of Operations Research 26 (2016), Number 2, 243-260 DOI: INTERACTIVE FUZZY GOAL PROGRAMMING APPROACH IN MULTI-RESPONSE STRATIFIED SAMPLE SURVEYS Neha GUPTA Department of Statistics & Operations Research, Aligarh Muslim University, Aligarh, India ngngupta4@ Irfan ALI Department of Statistics & Operations Research, Aligarh Muslim University, Aligarh, India Abdul BARI Department of Statistics & Operations Research, Aligarh Muslim University, Aligarh, India bariamu2k3@ Received: October 2014 / Accepted: February 2015 Abstract: In this paper, we applied an Interactive Fuzzy Goal Programming (IFGP) approach with linear, exponential and hyperbolic membership functions, which focuses on maximizing the minimum membership values to determine the preferred compromise solution for the multi-response stratified surveys problem, formulated as a MultiObjective Non Linear Programming Problem (MONLPP), and by linearizing the nonlinear objective functions at their individual optimum solution, the problem is approximated to an Integer Linear Programming Problem (ILPP). A numerical example based on real data is given, and comparison with some existing allocations viz. Cochran’s compromise allocation, Chatterjee’s compromise allocation and Khowaja’s compromise allocation is made to demonstrate the utility of the approach. Keywords: Compromise Allocation, Coefficient of Variation, Interactive Fuzzy Goal Programming, Optimum Allocation. MSC: 62D05. 244 N. Gupta, I. Ali, / Interactive Fuzzy Goal Programming Approach 1. INTRODUCTION In statistics, one of the most commonly used technique in all fields of scientific investigation is stratified sampling. In statistical surveys, when subpopulations within an overall population vary, it is advantageous to sample each subpopulation (stratum) independently. Stratification is the process of dividing members of the population into homogeneous subgroups .
