A 2-dimension linguistic Pythagorean fuzzy decision-making method with application to unmanned aerial vehicle contribution assessment.

Assessing the contribution of an unmanned aerial vehicle to the effectiveness of a swarm is a challenging problem, as it depends heavily on expert judgments that are often subjective, imprecise, and expressed with varying levels of confidence. Existing decision-making methods can capture evaluative uncertainty but generally fail to represent the reliability of those evaluations within a unified framework. To address this gap, this study introduces a 2-dimension linguistic Pythagorean fuzzy variable, which simultaneously represents an expert's linguistic evaluation and the confidence attached to that evaluation under the Pythagorean fuzzy condition. The fundamental operational rules, score and accuracy functions, and aggregation operators for 2-dimension linguistic Pythagorean fuzzy variables are developed, and their algebraic properties are formally established. Building on this representation, a multi-criteria decision-making method is proposed for unmanned aerial vehicle contribution assessment. A practical case study demonstrates that the method produces results that are consistent with established approaches, strongly correlated in ranking performance, and sensitive to differences in expert confidence, thereby providing both reliability and interpretability. Nevertheless, the current study assumes fixed linguistic term sets and a static confidence dimension, and the case study is limited to a small number of evaluation criteria. Future research will address calibration of linguistic scales, dynamic updating of confidence, and broader validation across domains. Overall, the proposed approach offers a structured and reliable tool for evaluating unmanned aerial vehicle contributions in swarm operations and enriches the methodological foundations for decision-making under uncertainty.