Expert Elicitation of Fuzzy Membership Functions of Linguistic Terms: A Fire Evacuation Case Study

Abstract

Decision-making in complex, uncertain environments, like emergency evacuations, often relies on the use of linguistic terms to express subjective judgments. However, the inherent ambiguity of these linguistic terms, coupled with the variability of expert opinions, poses a significant challenge for accurate decision-making. Membership functions (MFs) are essential tools for quantifying and representing the meaning of these linguistic terms, allowing for the computational processing of subjective judgments. Existing methods for eliciting MFs of these terms struggle to capture the inherent variability and probabilistic nature of expert opinions, hindering the accurate representation of uncertainty. Existing methods for eliciting membership functions (MFs) of these terms struggle to capture the inherent variability and probabilistic nature of expert opinions, hindering accurate representation of uncertainty. This study propose a framework for eliciting MFs of probabilistic linguistic terms using the Interval Estimation (IE) technique. The procedure integrates a graphic survey to construct MFs that fulfils the definition of Triangular Fuzzy Number (TFN). This approach allows experts to directly express their uncertainty ranges, ensuring the resulting MFs reflect both their individual perceptions and the overall probabilistic distribution of opinions. A case study eliciting psychological responses in fire evacuation scenarios is utilized to demonstrate the utility of our proposed framework. The developed MFs were integrated into a Bayesian Network (BN) decision model. The performance analysis indicated by sensitivity values confirms the stability and robustness of the BN model parameters, thereby validating the rationality and meaningfulness of the expert-elicited MFs. The resulting MFs demonstrated a significant improvement in capturing the variability of psychological responses compared to traditional methods. This robust methodology provides a practical tool for developing expert-driven fuzzy linguistic scales tailored to specific domains thus offering practical applications for decision-making in uncertain environments.