Purpose
This study investigates the drivers of consumer engagement and behavioral intentions in augmented reality (AR) enabled e-commerce environments, with a specific focus on how cognitive and emotional mechanisms jointly shape consumer responses to AR features.

Methods
Grounded in the Stimulus-Organism-Response (S-O-R) framework, the study employs a dual-model, data-driven approach. A Partial Least Squares Structural Equation Model (PLS-SEM) using data from 312 active AR users is applied to examine linear cognitive-behavioral relationships influencing purchase intention. To capture nonlinear and subconscious effects, a Fuzzy Logic model based on the S-O-R framework is developed based on responses from 487 online consumers. In addition, cluster analysis is conducted to identify distinct consumer engagement profiles.

Results
The findings reveal that perceived usefulness (β = 0.293, p < 0.001), enjoyment (β = 0.206, p < 0.01), and AR engagement (β = 0.142, p < 0.05) are significant drivers of purchase intention, with the model explaining 41% of the variance. The Fuzzy Logic analysis further demonstrates that emotional satisfaction and interactivity mediate the effects of AR exposure on brand trust and loyalty, even among consumers with limited conscious awareness of AR use. Three consumer segments-AR Explorers, Skeptical Users, and Passive Observers - are identified, highlighting heterogeneity in AR driven engagement behaviors.

Originality/Value
This research advances the augmented reality and digital marketing literature by integrating SEM and Fuzzy Logic to simultaneously capture explicit cognitive evaluations and implicit emotional responses to AR. By revealing nonlinear engagement mechanisms and distinct consumer archetypes, the study offers a more comprehensive explanation of how AR technologies influence consumer engagement and behavioral intentions in digital retail contexts.