Within fine-grained Aspect-Based Sentiment Analysis, one of the critical subtasks is Aspect Sentiment Triplet Extraction, which aims to extract all triplets from user comments, including aspect terms, associated opinion terms, and the corresponding sentiment polarity. Previous approaches to the study of Aspect Sentiment Triplet Extraction (ASTE) tasks have primarily used an end-to-end strategy based on filling tables. However, these methods typically overlook the multi-dimensional features of linguistic expressions and the associations between words. As a result, valuable interactive information is lacking between extracting aspect terms and opinion terms. To address the above problem, we propose a perceptive dual-graph semantic integration network (PDGSIN). To achieve deeper semantic extraction of the sentence, we employ two graph convolutional networks (PosGCN and SynGCN) to capture part-of-speech relations and syntactic dependencies from the dual graphs (part-of-speech graphs and syntactic dependency graphs) of a sentence, respectively. Meanwhile, we design a graph feature fusion mechanism (GFFM) to inject part-of-speech and syntactic dependency features into BERT coding so that the coding contains more thorough and more prosperous semantic features. In addition, we apply a structured perception classifier (SPC) to extract triplets by making full use of the text's semantic and structural information. We conduct numerous experiments on standard datasets. The results reveal that our proposed method has significant performance advantages and high practical value.