Quadri-Partitioned Neutrosophic Programming Approach for Efficient Mixed Allocation in Multivariate Nonlinear Stratified Sampling: A DEA Perspective

Abstract

Efficient sample allocation in multivariate stratified surveys is a challenging mult objective optimization problem, particularly when parameters are imprecise and the survey design must balance multiple conflicting criteria. This paper introduces a novel Quadri-partitioned Neutrosophic Programming (QNP) approach for mixed allocation in multivariate nonlinear stratified sampling, integrated with Data Envelopment Analysis (DEA) for efficiency evaluation. The proposed framework extends traditional neutrosophic sets by incorporating a fourth component contradiction enabling more nuanced modeling of uncertainty, indeterminacy, and inconsistency in stratum parameters such as standard deviations, costs, and budget constraints. The QNP model transforms the mult objective allocation problem into a single-objective neutrosophic optimization problem using truth, indeterminacy, falsity, and contradiction membership functions. DEA is then employed to assess the relative efficiency of competing allocation strategies across strata. Real data from a national health survey comprising 25 strata and four health indicators are used to validate the approach. Results demonstrate that the QNP-based mixed allocation achieves a 15.3% reduction in weighted sampling variance compared to classical compromise allocation, with an average efficiency score of 0.94 across all strata. Comparative analysis with fuzzy, intuitionistic fuzzy, and single valued neutrosophic approaches confirms the superiority of Quadri-partitioned modeling. The integration of DEA provides valuable managerial insights for survey planners.