Abstract
In this paper, we investigated the notion of a linear Diophantine fuzzy set (LDFS) by using the concept of a score function to build the LDF-score left (right) ideals and LDF-score (0,2)-ideals in an AG-groupoid. We used these newly developed LDF-score ideals to characterize an AG-groupoid. We then use the proposed structure in multiattribute decision-making by considering bridge design selection and artificial intelligence-based chatbot selection.