Multiobjective intuitionistic fuzzy programming under pessimistic and optimistic applications in multivariate...

Area of Science:

• Statistics
• Survey Methodology
• Operations Research

Background:

• Multivariate stratified sampling is crucial for estimating population means efficiently.
• Handling nonresponse in surveys presents significant challenges to data accuracy.
• Optimizing sample allocation under budget constraints is a key issue in survey design.

Purpose of the Study:

• To develop a compromise allocation method for multivariate stratified sampling that accounts for both complete response and nonresponse.
• To formulate the sampling problem as a mathematical programming problem for estimating p-population means.
• To apply intuitionistic fuzzy programming for determining optimal sample allocations.

Main Methods:

• Mathematical programming formulation for multivariate stratified sampling with nonresponse.
• Intuitionistic fuzzy programming (IFP) with optimistic and pessimistic strategies.
• Simulation study using Stratify R software.
• Optimization using Lingo-18 software.

Main Results:

• The study successfully formulates and solves the compromise allocation problem for multivariate stratified sampling with nonresponse.
• Intuitionistic fuzzy programming provides effective strategies for sample allocation under fixed costs.
• Simulation results demonstrate the applicability and completeness of the proposed solution process.

Conclusions:

• The proposed compromise allocation method enhances the estimation of population means in the presence of nonresponse.
• This approach is valuable for optimizing survey designs in fields like wildlife, agriculture, and marketing.
• The study contributes to better national planning policies for survey data collection and analysis.