Sampling of multiple variables based on partial order set theory

TL;DR

This paper introduces a novel ranked set sampling method that utilizes partial order set theory to rank multiple variables simultaneously, enhancing sampling efficiency for complex criteria.

Contribution

It proposes a new ranking approach based on linear extensions in partial order sets, extending previous ranked set sampling methods to handle multiple variables.

Findings

Method evaluated through simulations

Applied to case studies in economics and environmental pollution

Demonstrates improved sampling accuracy

Abstract

This paper is going to introduce a new method for ranked set sampling with multiple criteria. The method is based on a version of ranked set sampling, introduced by Panahbehagh et al. (2017), which relaxes the restriction of selecting just one individual variable from each ranked set. Under the new method for ranking, elements are ranked in sets based on linear extensions in partial order sets theory, where based on all the variables simultaneously. Results will be evaluated by some simulations and two real case study on economical, medicinal use of flowers and the pollution of herb-layer by Lead, Cadmium, Zinc and Sulfur in regions in the southwest of Germany.